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Several conjugate gradient (CG) parameters resulted in promising methods for optimization problems. However, it turns out that some of these parameters, for example, 'PRP,' 'HS,' and 'DL,' do not guarantee sufficient descent of the search direction. In this work, we introduce new spectral-like CG methods that achieve sufficient descent property independently of any line search (LSE) and for arbitrary nonnegative CG parameters. We establish the global convergence of these methods for four different parameters using Wolfe LSE. Our algorithm achieves this without regular restart and assumption of convexity regarding the objective functions. The sequences generated by our algorithm identify points that satisfy the first-order necessary condition for Pareto optimality. We conduct computational experiments to showcase the implementation and effectiveness of the proposed methods. The proposed spectral-like methods, namely nonnegative SPRP, SHZ, SDL, and SHS, exhibit superior performance based on their arrangement, outperforming HZ and SP methods in terms of the number of iterations, function evaluations, and gradient evaluations. [ABSTRACT FROM AUTHOR]

Conjugate gradient techniques are known for their simplicity and minimal memory usage. However, it is known that in the vector optimization context, the Polak-Ribi'ere-Polyak (PRP), Liu-Storey (LS), and Hestenes-Stiefel (HS) conjugate gradient (CG) techniques fail to satisfy the sufficient descent property using Wolfe line searches. In this work, we propose a variation of the PRP, LS, and HS CG techniques that we termed YPR, YLS, and YHS, respectively. These techniques exhibit the desirable property of sufficient descent without line search, except for the YHS which uses Wolfe line search for its sufficient descent property. Under certain standard assumptions and employing strong Wolfe conditions, we investigate the global convergence properties of the proposed techniques. The global convergence analysis extends beyond convexity assumption on the objective functions. Additionally, we present numerical experiments and comparisons to demonstrate the implementation, efficiency, and robustness of the proposed techniques. [ABSTRACT FROM AUTHOR]

In this paper, we propose a modified general inertial Mann algorithm and prove that it generates a sequence which converges weakly to a fixed point of a nonexpansive mapping in Hilbert spaces. Moreover, by using the viscosity method, we introduce a general inertial viscosity algorithm and prove that it generates a sequence which converges strongly to a common fixed point of a countable family of nonexpansive operators. We also derive schemes for solving constrained convex optimization, monotone inclusion, and nonsmooth convex optimization problems. Finally, we apply one of our proposed algorithms to solve image restoration problem. [ABSTRACT FROM AUTHOR]

In this work, two inertial algorithms for approximating common elements of the sets of solutions of three important problems are constructed. The first problem is a generalized mixed equilibrium one involving relaxed monotone mapping, the second is a zero problem of inverse strongly monotone mappings, while the third one is a fixed point problem of a family of relatively nonexpansive mappings. The first algorithm is a shrinking projection type for a common solution of all the three problems. The second is a generalized Alber projection free method for the second and the third problems. Each of the devised algorithms uses the conjugate gradient-like direction, which allows it to accelerate its iterates toward a solution of the problems. The strong convergence theorem for each of the algorithms is formulated and proved in a real 2 - uniformly convex and uniformly smooth Banach space. Additionally, the applications of our algorithms to convex optimization problems and image recovery problems are studied. The advantages and computational efficiency of our methods are analyzed based on their numerical performance in comparison to some of the existing and recently proposed methods using numerical example. [ABSTRACT FROM AUTHOR]

The approach described in this research is an exemplar‐based inpainting problem that combines a two‐stage structure tensor and image sparse representation to fill in any missing pixels. An important step is to select the filling order and local intensity smoothness, as well as to ensure that the structure is not destroyed. We employ a two‐stage structure tensor‐based priority for the filling order: finding the candidate patches and determining the appropriate weight of each candidate patch under the constraint of local patch consistency, then applying a blend of a sparse linear combination of candidate patches to fill in the missing region of the image. In addition, this technique may also be used for object removal. The proposed method yields results that are visually natural and qualitative. [ABSTRACT FROM AUTHOR]

In this work, we establish the closedness and convexity of the set of fixed points of equally continuous and asymptotically demicontractive mapping in the intermediate sense. We proposed an inertial hybrid projection technique for determining an approximate common solution to three significant problems. The first is the system of generalized mixed equilibrium problems with relaxed η−ζ$$ \eta -\zeta $$ monotone mappings, the second is the problem of fixed points of a countable family of equally continuous and asymptotically demicontractive mappings in the intermediate sense, and the third is of determining a point in a null space of a countable family of inverse strongly monotone mappings in Hilbert space. Based on these problems, we formulate a theorem and establish its strong convergence to their common solution. Additionally, we studied the applications of our algorithm to variational inequality problems and convex optimization problems. Finally, we numerically demonstrate the efficiency and robustness of our scheme. Several results available in the literature can be obtained as special cases of our result. [ABSTRACT FROM AUTHOR]

The purpose of the present paper is to construct a common solution of the split null point problem associated with the maximal monotone operators and the fixed point problem associated with a finite family of k‐demicontractive operators in Hilbert spaces. We compute the optimal common solution via inertial parallel hybrid algorithm under a suitable set of control conditions. The viability of parallel implementation of the algorithm is demonstrated for various theoretical as well as numerical results. The results presented in this paper improve various existing results in the current literature. [ABSTRACT FROM AUTHOR]

Nanofluids are used to achieve maximum thermal performance with the smallest concentration of nanoparticles and stable suspension in conventional fluids. The effectiveness of nanofluids in convection processes is significantly influenced by their increased thermophysical characteristics. However, this technology is not ended here; binary and ternary nanofluids are now used to improve the efficiency of regular fluids. Therefore, this paper aims to analyze the natural convection Newtonian ternary nanofluid flow in a vertical channel. The tri‐hybridized nanoparticles of zinc oxide ZnO, Aluminum oxide Al2O3, and titanium oxide TiO2 is dissolved in base fluid distilled water (DW) to form a homogenous suspension. The impact of thermal radiation, joule heating, and viscous dissipation are also assumed. The classical Newtonian ternary nanofluid model has been generalized by using fractal‐fractional derivative (FFD) operator. The generalized model has been discretized by using the Crank–Nicolson scheme and then solved by using computational software. To analyze the behavior of fluid flow and heat distribution in fluid, the obtained solution was computed numerically and then plotted in response to different physical parameters. It is noted from the figure that when the volume fraction ϕ reaches to 0.04 (4% of the base fluid), the ternary nanofluid flow shows a significant amount of enhancement in heat transfer rate as compared to binary and unary nanofluid flows. This enhancement in the rate of heat transfer leads to improve the thermophysical characteristics such as viscosity, thermal expansion, and heat capacity etc. of the base fluid. It is also worth mentioning here that the thermal field is also enhance with the higher values of Eckert number Ec$Ec$, radiation parameter Rd$Rd$, and joule heating parameter Jh${J_h}$. [ABSTRACT FROM AUTHOR]

The Caputo operator has recently gained popularity as a widely used operator in fractional calculus. The purpose of this current research is to develop a new operator by combining the Caputo and proportional derivatives, resulting in the constant proportional Caputo (CPC) fractional operator. To demonstrate the dynamic behavior of this newly defined operator, it was applied to the unsteady Oldroyd‐B fluid model. Additionally, the research considered an Oldroyd‐B fluid in a generalized Darcy medium, considering non‐uniform temperature, radiation, and heat generation. Analytical solutions for the proposed model were obtained and presented in graphical form using the computational software MATHCAD. The impact of various physical parameters was also examined through graphical analysis of velocity and temperature profiles, as well as a comparison between isothermal and non‐uniform temperature. In conclusion, this research found that the CPC fractional operator effectively explains the dynamics of the Oldroyd‐B fluid model with stable and strong memory effects, compared to the classical model. [ABSTRACT FROM AUTHOR]

This paper provides convergence analysis of some variants of the hybrid extragradient algorithm (HEA) in Hilbert spaces. We employ the HEA to compute the common solution of the equilibrium problem and split fixed-point problem associated with the finite families of k -demicontractive mappings. We also incorporate appropriate numerical results concerning the viability of the proposed variants with respect to various real-world applications. [ABSTRACT FROM AUTHOR]

Language is closely connected to the concepts of uncertainty and indeterminacy, as it functions as a fundamental tool for the expression and communication of information. Linguistic formulations possess inherent qualities of ambiguity, imprecision, and vagueness. The comprehension of language frequently hinges upon contextual factors, individual interpretation, and subjective viewpoints, resulting in ambiguities in comprehension. Neutrosophic-linguistic valued hypersoft sets (N-LVHS) play a pivotal role in decision-making by effectively managing linguistic uncertainty, modeling real-world complexity, and accommodating multidimensional information. In the realm of medical diagnosis and treatment, several limitations tied to language and indeterminacy persist. Patients often use vague or imprecise language to describe their symptoms, complicating the accurate identification of ailments. Moreover, diagnostic criteria are subjectively defined, leading to inconsistencies in diagnoses. Disease progression, characterized by its complexity and unpredictability, adds further indeterminacy in treatment planning. The variability in patient responses to treatments introduces uncertainties in outcome prediction. Inconclusive test results and limited clinical data may compound these challenges, underscoring the need for innovative approaches like N-LVHS to address these linguistic and indeterminacy-related limitations and improve the precision and efficacy of medical decision-making and treatment procedures. In constructing an N-LVHS framework for medical diagnosis and treatment, relevant factors, and linguistic terms characterizing medical conditions and treatments are identified. For example, disease severity could be described using terms such as "mild," "moderate," and "severe," while treatment effectiveness may be categorized as "low," "moderate," and "high." Each factor is then assigned neutrosophic values based on their measured impacts. This approach provides a more precise representation of the complex medical diagnostic and treatment landscape. The findings of this study have the potential to assist medical practitioners, researchers, and policymakers in optimizing medical diagnosis and treatment strategies, enhancing patient outcomes, and improving healthcare practices. [ABSTRACT FROM AUTHOR]

In this paper, we prove strong convergence theorem of the general inertial Mann–Halpern algorithm for nonexpansive mappings in the setting of Hilbert spaces. We also prove weak convergence theorem of the general inertial Mann algorithm for k-strict pseudo-contractive mappings in the setting of Hilbert spaces. These convergence results extend and generalize some existing results in the literature. Finally, we provide examples to verify our main results. [ABSTRACT FROM AUTHOR]

The complex process of decision-making is addressed in this study, especially when dealing with diverse factors and input from several specialists. In the context of m-polar interval-valued neutrosophic hypersoft sets (m-PIVNHSSs), the paper proposes innovative adaptations of the correlation coefficient (CC) and weighted correlation coefficient (WCC), drawing on correlation analysis in statistics and engineering. The goal is to improve decision-making processes in scenarios with complicated features and input from several specialists. Through defined theorems and claims, the study offers a solid mathematical framework and presents methods based on CC and WCC to address decision-making complexity. These strategies show promise for enhancing decision accuracy in circumstances involving a wide range of features and expert inputs. AHP, TOPSIS, and other strategies that are now used might also be extended, according to the research. AHP, TOPSIS, and VIKOR are three possible methodologies that might be used to the m-PIVNHSSs environment, according to the research, opening opportunities for additional breakthroughs in the decisionmaking sector. [ABSTRACT FROM AUTHOR]

Language, as an abstract system and a creative act, possesses inherent complexity due to its contextual nature and the variability of its meaning. The context of language is shaped by an individual's empirical knowledge, derived from observation and experience. Decision-making challenges related to language encompass both quantitative and qualitative factors, which further contribute to the intricacy of the process. Decision-making challenges may involve both quantitative and qualitative aspects of further subdivided attributes. However, linguistic knowledge cannot be easily quantified by existing methods. Therefore, current methods are ineffective in handling linguistic knowledge. Using mathematical values, such as fuzzy, intuitionistic, and neutrosophic, in decision-making problems without following linguistic knowledge rules can result in vagueness and imprecision. To address these issues, this paper presents a comprehensive generic model. The model introduces the linguistic set structure of the hypersoft set (LHSS) as a solution for decision-making problems. The definition of fundamental operations, including AND, NOT, OR complement, and negation, is proposed alongside illustrative examples and their respective properties. Additionally, operational laws for the linguistic hypersoft set are introduced to effectively address decision-making challenges. By implementing the proposed aggregate operators and operational laws, linguistic quantifiers can be converted into numerical values, thereby enhancing the accuracy and precision of the hypersoft set structure in decision-making scenarios. [ABSTRACT FROM AUTHOR]

Engine Oil is a widely used fluid in engineering problems, particularly to enhance the rate of heat transfer when these working fluids play a fundamental role. We consider engine oil as a base fluid and the suspension of different shaped (Spherical cylindrical and platelet) nanoparticles dispersed uniformly in the base fluid to enhance the working capability of engine oil. The spherical shape CuO , platelet shape Al 2 O 3 and cylindrical shape TiO 2 nanoparticles are added in engine oil to constitute tri-hybrid nanofluid aiming at obtaining better thermal performance. Furthermore, we also analyze the Jeffery tri-hybrid nanofluid in a rotating frame over an infinite vertical plate. More precisely, the classical model of Jeffery tri-hybrid nanofluid is transformed into a time-fractional model by applying the newly developed constant proportional Caputo fractional derivatives. Sharp numerical results are obtained applying a Laplace transform steered approach. All the flow parameters are highlighted through graphs via MATHCAD. Furthermore, a comparative analysis between nanofluid, hybrid nanofluid and tri-hybrid nanofluid has been performed showing that tri-hybrid nanofluid has good thermal performance. The solutions of the constant proportional operator are discussed classically by taking fractional parameter α → 1. Moreover, some engineering quantities have been calculated and presented in tables. During the analysis we dispersing the mixture of nanoparticles in engine oil base fluid enhanced the heat transfer up-to18.72% which can efficiently improve the lubricity of the engine oil. [ABSTRACT FROM AUTHOR]

An option is a financial derivative that can help investors hedge risk or speculate by taking on more risk for more profit. Therefore, option pricing models have played an important role in supporting investors. The option price is influenced by the volatility of an underlying asset return, which is impacted by both positive and negative information. The volatility of the option price is considered an important factor for approximating option, especially in short-term option trading. In this research, a fuzzy-TGARCH model is constructed to estimate volatility, which is used to calculate an option price in the stock market with a short-term maturity date. This proposed approach is described and analyzed by comparing the numerical results with those of other methods. The data in the SET50 market are used for observation. With this data, the proposed method performs well for ITM cases when time to maturity is 20 and 30 days. [ABSTRACT FROM AUTHOR]

This work presents a new three-term projection algorithm for solving nonlinear monotone equations. The paper is aimed at constructing an efficient and competitive algorithm for finding approximate solutions of nonlinear monotone equations. This is based on a new choice of the conjugate gradient direction which satisfies the sufficient descent condition. The convergence of the algorithm is shown under Lipschitz continuity and monotonicity of the involved operator. Numerical experiments presented in the paper show that the algorithm needs a less number of iterations in comparison with existing algorithms. Furthermore, the proposed algorithm is applied to solve signal recovery problems. [ABSTRACT FROM AUTHOR]

Nanofluids are used to achieve maximum thermal performance with the smallest concentration of nanoparticles and stable suspension in conventional fluids. The effectiveness of nanofluids in convection processes is significantly influenced by their increased thermophysical characteristics. Based on the characteristics of nanofluids, this study examines generalized Brinkman-type nanofluid flow in a vertical channel. Three different types of ultrafine solid nanoparticles such as GO, Al 2 O 3 , and TiO 2 are dispersed uniformly in regular water to form nanofluid.  Partial differential equations (PDEs) are used to model the phenomena. Fick's and Fourier's laws of fractional order were then used to formulate the generalized mathematical model. The exact solution of the generalized mathematical model has been obtained by the joint use of Fourier sine and the Laplace transform (LT) techniques. The obtained solution is represented in Mittag-Leffler function. To analyze the behavior of fluid flow, heat and mass distribution in fluid, the obtained solution was computed numerically and then plotted in response to different physical parameters. It is worth noting from the analysis that the heat transfer efficiency of regular water has been improved by 25% by using GO nanoparticles, 23.98% by using Al 2 O 3 , and 20.88% by using TiO 2 . [ABSTRACT FROM AUTHOR]

Cryptography is processing for securing communication between two people. The opponent wants to know the message that is encrypted using a secret key. Although the opponent can eavesdrop the message sent between the sender and the receiver, the opponent is unable to decrypt to read the message. Therefore, the secret key is very important. The sender and the receiver agree with the secret key in an insecure channel by using key distribution protocol such as the Diffie–Hellman protocol. Since quantum computer is coming soon, Diffie–Hellman protocol is not secure. We will develop a quantum key distribution protocol. The benefit of the quantum system is the quantum state that cannot copy by no‐cloning theorem. Thus, the opponent does not copy and keeps the message that is quantum. In this paper, a novel quantum key distribution protocol between two people (Alice and Bob) based on quantum operators is developed. The opponent (Eve) wants to know the secret key. Although Eve knows this quantum key distribution protocol, Eve does not behave similarly to Alice and Bob. For example, Eve eavesdrops Alice's quantum state that was sent to Bob, and Eve sends another quantum state. Therefore, we cannot control Eve's behavior. So we give the upper bound of mutual information between the user and opponent by using Holevo's bound. We verify the usual security definition for quantum key distribution that is equality‐and‐uniformity and privacy in the mutual information sense. [ABSTRACT FROM AUTHOR]

Engine Oil is a widely used fluid in engineering problems, particularly to enhance the rate of heat transfer when these working fluids play a fundamental role. We consider engine oil as a base fluid and the suspension of different shaped (Spherical cylindrical and platelet) nanoparticles dispersed uniformly in the base fluid to enhance the working capability of engine oil. The spherical shape CuO , platelet shape Al 2 O 3 and cylindrical shape TiO 2 nanoparticles are added in engine oil to constitute tri-hybrid nanofluid aiming at obtaining better thermal performance. Furthermore, we also analyze the Jeffery tri-hybrid nanofluid in a rotating frame over an infinite vertical plate. More precisely, the classical model of Jeffery tri-hybrid nanofluid is transformed into a time-fractional model by applying the newly developed constant proportional Caputo fractional derivatives. Sharp numerical results are obtained applying a Laplace transform steered approach. All the flow parameters are highlighted through graphs via MATHCAD. Furthermore, a comparative analysis between nanofluid, hybrid nanofluid and tri-hybrid nanofluid has been performed showing that tri-hybrid nanofluid has good thermal performance. The solutions of the constant proportional operator are discussed classically by taking fractional parameter α → 1. Moreover, some engineering quantities have been calculated and presented in tables. During the analysis we dispersing the mixture of nanoparticles in engine oil base fluid enhanced the heat transfer up-to18.72% which can efficiently improve the lubricity of the engine oil. [ABSTRACT FROM AUTHOR]

In this manuscript, we investigate and approximate common fixed points of two nonself asymptotically nonexpansive mappings in the setting of CAT(0) spaces. We provide three examples and conduct numerical experiments to show the implementation of the approximation schemes. Our results extend and improve the related results in the literature. [ABSTRACT FROM AUTHOR]

The main objective is to apply the concept of newly developed idea of the fractional‐order derivative of the Rabotnov fractional–exponential function in fluid dynamics. In this article, a newly developed idea of the fractional‐order derivative of the Rabotnov fractional–exponential function and the nonsingular kernel has been applied to study viscous fluid flow in the presence of an applied magnetic field. The flow is considered over an infinite vertical plate moving with arbitrary velocity. The modeled problem is transformed into a nondimensional form via dimensionless analysis, and then the Laplace transform method is applied for the solution of the problem. Due to the complexity in Laplace inversion, a strong numerical inversion procedure, namely, Zakian's algorithm, has been used, and the results are computed in various plots and tables. The corresponding discussion of results is included in detail. It is concluded that the generalized fractional‐order derivative is accurate and efficient for describing general fractional‐order dynamics in complex and power law phenomena. [ABSTRACT FROM AUTHOR]

In this article, an Ishikawa iteration scheme is modified for b$$ b $$‐enriched nonexpansive mapping to solve a fixed point problem and a split variational inclusion problem in real Hilbert spaces. Under some suitable conditions, we obtain convergence theorem. Moreover, to demonstrate the effectiveness and performance of proposed scheme, we apply the scheme to solve a split feasibility problem and compare it with some existing iterative schemes. [ABSTRACT FROM AUTHOR]

This paper provides iterative construction of a common solution associated with the fixed point problem of an infinite family of |-demicontractive mappings, pseudomonotone equilibrium problem satisfying Lipschitz-type continuity and the split common null point problem. We propose an iterative algorithm that combines the classical extragradient method with the inertial extrapolation technique. The analysis of the proposed algorithm is two-fold: firstly, we establish strong convergence results under suitable set of constraints and secondly we verify the viability of the proposed algorithm via numerical experiment with applications. [ABSTRACT FROM AUTHOR]

Fractional calculus gets more attention in applied and pure science from the last two decay due to their valuable contribution. Due to extensive applications of fractional derivatives, the main aim of this article is focused on the multi fractional comparative study of entropy generation of magnetohydrodynamic (MHD) flow of Casson nanofluid with slipping and ramped wall heating effect on the plate. Set of partial differential equations forms governing equation and by using constant proportional–Caputo hybrid (CPC), Atangana–baleanu (AB) and Caputo Fabrizio (CF) fractional derivative generalized the model. Using the Laplace transform approach, a closed form of the solution is attained. Entropy production for Casson nanofluid is explored and compared using triple fractional modelled and for four different nanoparticles. Furthermore, the Bejan number is compared for the previously mentioned fractional derivatives. The graphs depict the effect of several parameters on the minimization and maximisation of multi generalised entropy generation. Instead of Atangana–baleanu and Caputo Fabrizio fractional operators, the newly proportional Caputo hybrid operator has a strong memory effect. It is concluded that CPC fractional model is more realistic then other two fractional model in case of ramped wall temperature while in case of isothermal wall temperature the results are vice versa. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a derivative‐free iterative method for finding the solutions of convex constrained nonlinear equations (CCNE) using the projection strategy. The new approach is free from gradient evaluations at each iteration. Also, the search direction generated by the proposed method satisfies the sufficient descent property, which is independent of the line search. Compared with traditional methods for solving CCNE that assumes Lipschitz continuity and monotonicity to establish the global convergence result, an advantage of our proposed method is that the global convergence result does not require the assumption of Lipschitz continuity. Moreover, the underlying operator is assumed to be pseudomonotone, which is a milder condition than monotonicity. As an applications, we solve the LASSO problem in compressed sensing. Numerical experiments illustrate the performances of our proposed algorithm and provide a comparison with related algorithms. [ABSTRACT FROM AUTHOR]

In this paper, a Halpern–Tseng-type algorithm for approximating zeros of the sum of two monotone operators whose zeros are J-fixed points of relatively J-nonexpansive mappings is introduced and studied. A strong convergence theorem is established in Banach spaces that are uniformly smooth and 2-uniformly convex. Furthermore, applications of the theorem to convex minimization and image-restoration problems are presented. In addition, the proposed algorithm is used in solving some classical image-recovery problems and a numerical example in a Banach space is presented to support the main theorem. Finally, the performance of the proposed algorithm is compared with that of some existing algorithms in the literature. [ABSTRACT FROM AUTHOR]

In 2012, Rivaie et al. introduced RMIL conjugate gradient (CG) method which is globally convergent under the exact line search. Later, Dai (2016) pointed out abnormality in the convergence result and thus, imposed certain restricted RMIL CG parameter as a remedy. In this paper, we suggest an efficient RMIL spectral CG method. The remarkable feature of this method is that, the convergence result is free from additional condition usually imposed on RMIL. Subsequently, the search direction is sufficiently descent independent of any line search technique. Thus, numerical experiments on some set of benchmark problems indicate that the method is promising and efficient. Furthermore, the efficiency of the proposed method is demonstrated on applications arising from arm robotic model and image restoration problems. [ABSTRACT FROM AUTHOR]

In this paper, we study the split feasibility problem with multiple output sets in Hilbert spaces. For solving the aforementioned problem, we propose two new self-adaptive relaxed CQ algorithms which involve computing of projections onto half-spaces instead of computing onto the closed convex sets, and it does not require calculating the operator norm. We establish a weak and a strong convergence theorems for the proposed algorithms. We apply the new results to solve some other problems. Finally, we present some numerical examples to show the efficiency and accuracy of our algorithm compared to some existing results. Our results extend and improve some existing methods in the literature. [ABSTRACT FROM AUTHOR]

In the setting of Hilbert spaces, we show that a hybrid steepest-descent algorithm converges strongly to a solution of a convex minimization problem over the fixed point set of a finite family of multivalued demicontractive mappings. We also provide numerical results concerning the viability of the proposed algorithm with possible applications. [ABSTRACT FROM AUTHOR]

We apply the concept of quasilinearization to introduce some enriched classes of Banach contraction mappings and analyse the fixed points of such mappings in the setting of Hadamard spaces. We establish existence and uniqueness of the fixed point of such mappings. To approximate the fixed points, we use an appropriate Krasnoselskij-type scheme for which we establish ∆ and strong convergence theorems. Furthermore, we discuss the fixed points of local enriched contractions and Maia-type enriched contractions in Hadamard spaces setting. In addition, we establish demiclosedness-type property of enriched nonexpansive mappings. Finally, we present some special cases and corresponding fixed point theorems. [ABSTRACT FROM AUTHOR]

In this paper, relaxed and relaxed inertial modified Tseng algorithms for approximating zeros of sum of two monotone operators whose zeros are fixed points or J-fixed points of some nonexpansive-type mappings are introduced and studied. Strong convergence theorems are proved in the setting of real Banach spaces that are uniformly smooth and 2-uniformly convex. Furthermore, applications of the theorems to the concept of J-fixed point, convex minimization, image restoration and signal recovery problems are also presented. In addition, some interesting numerical implementations of our proposed methods in solving image recovery and compressed sensing problems are presented. Finally, the performance of our proposed methods are compared with that of some existing methods in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we construct three new extragradient-type iterative methods for solving variational inequalities in real Hilbert spaces. The proposed iterative methods are functionally equivalent to the extragradient method, which is used to solve variational inequalities in an infinite-dimensional real Hilbert space. The main advantage of these iterative methods is that they use a simple step size rule based on operator information instead of the Lipschitz constant or any line search method. Three strong convergence theorems are well proved, corresponding to the proposed methods by allowing certain control parameter conditions. Finally, we present some numerical experiments to verify the efficacy and superiority of the proposed iterative methods. [ABSTRACT FROM AUTHOR]

In this article, we present two Tseng's methods for finding a singularity point of an inclusion problem which is defined by means of a sum of a single-valued vector field and a multivalued vector field on a Hadamard manifold. Under standard assumptions, we prove any sequence generated by the proposed methods converges to a singularity point, whenever it exists. Moreover, applications to convex minimization problems and variational inequality problems are provided. [ABSTRACT FROM AUTHOR]

The multiple-sets split feasibility problem (MSSFP) requires finding a point closet to a family of closed convex sets in one space such that its image under a linear transformation will be closest to another family of closed convex sets in the image space. Motivated by the ball-relaxed projection algorithm proposed by Yu et al. for the split feasibility problem (SFP), in this paper, we introduce ball-relaxed projection algorithms for solving the MSSFP. Instead of the level sets or half-spaces, our algorithms require computing the orthogonal projections onto closed balls. We establish weak and strong convergence of the proposed algorithms to a solution of the MSSFP. Finally, we provide preliminary numerical experiments to show the efficiency and the implementation of our method. [ABSTRACT FROM AUTHOR]

To control the complicated rheological behavior of fluid models, several mathematical approaches have been established. Empirical, statistical, iterative, and analytical approaches are used to study such mathematical models. Consequently, this paper provides an analytical analysis and assessment of the Laplace, and Sumudu transforms for the unsteady MHD flow prediction of a second‐grade hybrid nanofluid in a rotating frame. The mathematical model is built using a nonfractional technique with ramping conditions. To explore the velocity field and heat transfer, we used Laplace and Sumudu transforms to uncover the unseen characteristics of magnetized second‐grade hybrid nanofluid flow. For the purposes of comparison, a graphical picture is given that represents successful outcomes in the literature for the first time. In conclusion, numerical simulations show that the derived outlines of velocity and temperature fields using Sumudu and Laplace transformations correspond well. In addition, the variation of velocity of fluid against time is reported for ramped wall temperature, while it is constant for isothermal wall temperature. [ABSTRACT FROM AUTHOR]

This study provides the exact solutions of couple stress fluid (CSF) in a channel. The CSF is bounded by two plates in which the lower plate is moving with constant velocity Uo and the upper plate is fixed. The influence of the external pressure gradient is considered on the CSF fluid. To transform the classical CSF model, we have introduced three approaches to fractional derivatives, (a) Caputo (b) Caputo–Fabrizio (CF), and (c) Atangana–Baleanu (AB) fractional definitions. Exact solutions have been obtained using the Laplace and finite Fourier sine transforms jointly. Furthermore, the effect of different fractional derivatives is compared, and the results are shown in graphs. Moreover, parameters that affect the CSF motion are discussed in the graphs using the computational software MATHCAD. The most important outcome of the given study is the comparison of Caputo, CF, and AB fractional models with the classical CSF model. From the comparison, it can be noticed that AB fractional model discusses the dynamics of the CSF with a good memory effect as compared to Caputo and CF fractional operators. The CSF model can be reduced to Newtonian fluid as a limiting case and also investigated solutions in the absence of external pressure. Finally, Skin friction is evaluated for lower and upper plates, and the obtained results presented in tabular form. [ABSTRACT FROM AUTHOR]

In this article, we propose a hybrid iterative scheme with strong convergence property for solving variational inequality problems. The algorithm uses a self-adaptive stepsize defined using a simple updating rule. Therefore, the method does not require prior knowledge of the Lipschitz constant of the underlying operator. We consider a more general set of operators as the underlying operators. Moreover, we derived a fixed stepsize scheme from the proposed method. Under some suitable conditions, we show the strong convergence of the iterates generated by the proposed and the derived algorithms. Furthermore, we present numerical experiments to illustrate the computational performance of the proposed algorithm in comparison with some of the existing algorithms in the literature. Additionally, as an application, we use the proposed algorithm to solve the problem of recovering an original signal from a noisy signal [ABSTRACT FROM AUTHOR]

This paper concentrated on the multiple generalized report of entropy generation of MHD Casson fluid via Caputo–Fabrizio (CF), Caputo (C), and Atangana–Baleanu (AB) fractional derivative. The ramped wall temperature on the plate while slipping condition on fluid velocity is considered. The mathematical model is made up of a collection of partial differential equations having physical boundaries. Triple fractional definitions are used to generalize the model and solve via joint Laplace and Zakian's numerical algorithm. The fractional results of entropy generation, velocity profile, temperature profile and Bejan number are also evaluated and compared for all three mentioned fractional operators as an objective of the present study. Entropy production can be maximize/ minimize through various physical parameters. The rate of heat transmission may be controlled by increasing the Prandtl number in isothermal temperature and boosting with the ramping wall temperature. It is indicated that Caputo model has maximum velocity and entropy generation in case of isothermal temperature besides Caputo–Fabrizio, and Atangana–Baleanu, while in case of ramped temperature, the phenomena is revised. The combined influence of slipping condition and ramped wall temperature rapidly boosts Casson fluid's velocity and entropy generation. [ABSTRACT FROM AUTHOR]

The generalized and optimal sequence of weights on a progressive‐iterative approximation method with memory for least square fitting (GOLSPIA) improves the MLSPIA method by extends to the multidimensional data fitting. In addition, weights of the moving average are varied between iterations, using the three optimal sequences of weights derived from the singular values of the collocation matrix. It is proved that a series of data fitting with an appropriate alternative of weights converge to the solution of least square fitting. Moreover, the convergence rate of the new method is faster than that of the MLSPIA method. Some examples and applications in this paper show the efficiency and effectiveness of the GOLSPIA method. [ABSTRACT FROM AUTHOR]

Numerical simulations of non-linear Casson nanofluid flow were carried out in a microchannel using the fractal-fractional flow model. The nano-liquid is prepared by dispersing Cadmium Telluride nanoparticles in common engine oil. Using relative constitutive equations, the system of mathematical governing equations has been formulated along with initial and boundary conditions. Dimensionless variables have been used to obtain the non-dimensional form of the governing equations. The fractal-fractional model has been obtained by employing the fractal-fractional operator of the exponential kernel. As the exact solution of the non-linear fractal-fractional model is very tough to find, therefore the formulated model has been solved numerically via the Crank-Nicolson scheme. Various plots are generated for the inserted parameters. From the analysis, it has been observed that a greater magnitude of the electro-kinetic parameter slows down the fluid's velocity. It is also worth noting that the fractional and classical models can also be derived from the fractal-fractional model by taking the parameters tend to zero. From the analysis, it is also observed that in response to 0.04 volume fraction of cadmium telluride nanoparticles, the rate of heat transfer (Nusselt number) and rate of mass transfer (Sherwood number) increased by 15.27% and 2.07% respectively. [ABSTRACT FROM AUTHOR]

With the help of CN-inequality, we study fixed point of multi-valued mappings with closed bounded images and establish some strong convergence theorems involving a countable family of demicontractive mappings in Hadamard spaces. Furthermore, we use the established theorems to deduce some theorems involving a family of minimization problems, variational inequality problems, and monotone inclusion problems. We finally give examples to illustrate the results. The results obtained herein generalise some recent results in the literature. [ABSTRACT FROM AUTHOR]

This study presents two inertial type extragradient algorithms for finding a common solution to the monotone variational inequalities and fixed point problems for ρ$$ \rho $$‐demicontractive mapping in real Hilbert spaces. We provide inertial type iterative algorithms with self‐adaptive variable step size rules that do not require prior knowledge of the operator value. Our algorithms employ a basic step size rule, which is derived by certain computations at each iteration. Without previous knowledge of the operators Lipschitz constant, two strong convergence theorems were obtained. Finally, we present a number of numerical experiments to evaluate the efficacy and applicability of the proposed algorithms. The conclusions of this study on variational inequality and fixed point problems support and extend previous findings. [ABSTRACT FROM AUTHOR]

This paper provides iterative construction of a common solution associated with a class of equilibrium problems and split convex feasibility problems. In particular, we are interested in the equilibrium problems defined with respect to the pseudomonotone and Lipschitz-type continuous equilibrium problem together with the generalized split null point problems in real Hilbert spaces. We propose an iterative algorithm that combines the hybrid extragradient method with the inertial acceleration method. The analysis of the proposed algorithm comprises theoretical results concerning strong convergence under suitable set of constraints and numerical results concerning the viability of the proposed algorithm with respect to various real-world applications. [ABSTRACT FROM AUTHOR]

This article aims to study entropy generation and heat transfer due to free convection. Two types of base fluids (water and kerosene oil) are taken with a suspension of titanium alloy nanoparticles. An external magnetic field is applied in a perpendicular direction and the induced magnetic field is neglected. Scientific analysis is performed on magnetohydrodynamic flow through a Darcy medium. Free convection and the sudden motion of the heated plate cause the fluid to flow. The problem is formulated in terms of differential equations with associated physical conditions. Relations for entropy generation and Bejan numbers are also provided. The Laplace transform technique has been used for finding the exact solution to the problem. Results are plotted using Mathcad software and a comparison is made between water-titanium alloy and kerosene oil-titanium alloy nanoparticles for velocity, temperature, entropy generation, and Bejan number. It is concluded that kerosene oil base fluid has a greater velocity and temperature profile in all parametric studies as compared to water-based fluid. While in the case of entropy generation and Bejan number, near to the plate and for away the plate the behaver is distinct. Entropy generation and Bejan number are boosting up via using different base fluid. For larger estimation of Brinkman number, both Bejan number and entropy rate have the opposite effect. The volume fraction of nanofluid enhance the rate of heat transfer in case of both nanofluid. While the water base nanofluid enhance the rate of heat transfer up to 19.14% and kerosene oil base fluid is enhanced up to 30.01%. [ABSTRACT FROM AUTHOR]

In this paper, the potential differential game concept introduced by Fonseca-Morales and Hernández-Lerma (2018) is used in analyzing stabilization problems for n-player noncooperative capital accumulation games (CAGs). By first identifying a CAG as a potential game, an associated optimal control problem (OCP) of the CAG is obtained, whose optimal solution is an open-loop Nash equilibrium for the CAG. Compared with a saddle-point stability condition obtained for undiscounted CAG in the literature, a sufficient and easily verifiable condition is obtained for both discounted and undiscounted CAGs. In addition, the concept allows the turnpike property obtained for OCPs in Trélat and Zuazua (2015) to be verified for CAGs. Lastly, an illustrative example is given to verify the latter stability result for some CAGs. [ABSTRACT FROM AUTHOR]

In this paper, we propose a hybrid conjugate gradient method for unconstrained optimization, obtained by a convex combination of the LS and KMD conjugate gradient parameters. A favourite property of the proposed method is that the search direction satisfies the Dai–Liao conjugacy condition and the quasi-Newton direction. In addition, this property does not depend on the line search. Under a modified strong Wolfe line search, we establish the global convergence of the method. Numerical comparison using a set of 109 unconstrained optimization test problems from the CUTEst library show that the proposed method outperforms the Liu–Storey and Hager–Zhang conjugate gradient methods. [ABSTRACT FROM AUTHOR]

We propose structured spectral gradient algorithms for solving nonlinear least squares problems based on a modified structured secant equation. The idea was to integrate more details of the Hessian of the objective function into the standardized spectral parameters with the goal of improving numerical efficiency. We safeguard the structured spectral parameters to avoid negative curvature search direction. The sequence of the search direction generated by the respective proposed algorithm satisfies the sufficient descent condition. Using a nonmonotone line search strategy, we establish the global convergence of the proposed algorithms under some standard assumptions. Numerical experiments on some benchmark test problems show that the proposed algorithms are efficient and outperform some existing competitors. [ABSTRACT FROM AUTHOR]

In the current research community, certain new fractional derivative ideas have been successfully applied to examine several sorts of mathematical models. The fractal fractional derivative is a novel concept that has been proposed in recent years. In the presence of heat generation, however, it is not employed for the free convection Couttee flow of the Casson fluid model. The core interest of the present analysis is to examine the Casson fluid under the influence of heat generation and magnetic field. The flow of the Casson fluid has been considered in between two vertical parallel plates. The distance between the plates is taken as l. The linear coupled governing equation has been developed in terms of classical PDEs and then generalized by employing the operator of the fractal-fractional derivative with an exponential kernel. The numerical solution of the proposed problem has been found employing the finite-difference technique presented by Crank–Nicolson. The Crank–Nicolson finite difference scheme has the advantage of being unconditionally stable and can be applied directly to the PDEs without any transformation to ODEs. This technique in sense of exponential memory has been revealed to be unreported in the literature for such a proposed problem. For graphical analysis, the graphs of velocity profile and thermal field have been plotted in response to several rooted parameters. For comparative analysis, the graphs for the parameter of fractal-fractional, fractional, and classical order have also been plotted. From the analysis, it has been found that the fractal-fractional order model has a large memory effect than the fractional-order and classical model due to the fractal order parameter. [ABSTRACT FROM AUTHOR]

This paper presents a hybrid conjugate gradient (CG) approach for solving nonlinear equations and signal reconstruction. The CG parameter of the approach is a convex combination of the Dai‐Yuan (DY)‐like and Hestenes‐Stiefel (HS)‐like parameters. Independent of any line search, the search direction is descent and bounded. Under some reasonable assumptions, the global convergence of the hybrid approach is proved. Numerical experiments on some benchmark test problems show that the proposed approach is efficient compared with some existing algorithms. Finally, the proposed approach is applied in signal reconstruction. [ABSTRACT FROM AUTHOR]