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The compromise solution of the multi‐criteria decision‐making (MCDM) problem by the existing VIKOR method for Pythagorean fuzzy sets (PyFSs) is not closest to the positive ideal solution. This is because the defining function for VIKOR does not obey the axioms for a dissimilarity measure. Thus in this context, the existing notion of dissimilarity measures and the VIKOR method are controversial. This study aims to provide a new dissimilarity measure and refine the VIKOR method for PyFSs accordingly. We define a new dissimilarity measure for PyFSs and refine the existing VIKOR method. We discuss the additional properties of dissimilarity measures and improve the ideas of remoteness and ranking indexes. We provide numerical examples to support the analysis and findings of our study. Finally, we solve the MCDM problems to illustrate the proposed method. [ABSTRACT FROM AUTHOR]

This study is focused to discuss the applications of non‐Newtonian fluid in engineering problems. In this article magneto‐hydrodynamics Casson fluid have taken with ramped temperature along an infinite plate with oscillations. In addition, in the present study we have considered the effect of porous media, chemical reaction, and radiation. Mostly, non‐Newtonian fluids uses for the lubrication purposes such as, engine oil, grease, and so forth. In the present study engine oil EO is selected as base fluid due to enormous applications in engineering. To enhance the rate of heat transfer two nanoparticles molybdenum disulfide (MoS2) and graphene oxide (GO) dispersed in EO. To transform the classical model into time fractional model Caputo–Fabrizio derivative have been used. To obtain the exact solutions for the proposed problem the Laplace transform is used. The solutions are depicted through graphs for various parameters to show the influence on fluid flow. Finally, we have compared the rate of heat transfer using different nanoparticles. It is worth noting that by using (MoS2) nanoparticle the heat transfer of engine oil can be enhanced up to 6.35% and by adding GO in regular engine oil the heat transfer can be enhanced up to 5.49%. [ABSTRACT FROM AUTHOR]

In this article, the study of magnetohydrodynamics Darcy‐Forchheimer flow is carried out. Viscous dissipation and thermal radiation are also deliberated for the flow system over a stretching and porous surface. Buongiorno model has been utilized to elaborate thermophoresis and Brownian dispersion impacts. The physical quantities such as viscosity, density, and specific heat play a key role in liquid flow behavior. The modeled equations are transformed to nonlinear ordinary differential equations and then solved by semi‐analytical technique HAM. It is found in this assessment that expanding estimations of the magnetic parameter builds Lorentz force and henceforth decreases the velocity profile. Moreover, velocity is also a reducing function of porosity and inertial parameters. The temperature of nanofluid diminishes with enhancement in the Prandtl number and porosity parameter while it increases with Brownian motion, radiation, thermophoretic parameters, and Brinkman number. The concentration profile is a growing function of the thermophoretic parameter and a reducing function of the Brownian motion parameter and Lewis number. [ABSTRACT FROM AUTHOR]

Despite the importance of divergence measures, the literature has not provided a satisfactory formulation for the case of q‐rung orthopair fuzzy set. This paper criticizes the existing attempts in terms of respect of the basic axioms of a divergence measure. Then new improved, axiomatically supported divergence measures for qROFSs are proposed. Additional properties of the new divergence measures are discussed to guarantee their good performance. The transformation relationships with entropy and dissimilarity measures are debated. The multiattribute border approximation area comparison decision method is extended based on the suggested divergence measures, and it is applied to the selection of all‐rounder cricketer for a team. [ABSTRACT FROM AUTHOR]

In this article, we offer two modifications of the modified forward‐backward splitting method based on inertial Tseng method and viscosity method for inclusion problems in real Hilbert spaces. Under standard assumptions, such as Lipschitz continuity and monotonicity (also maximal monotonicity), we establish weak and strong convergence of the proposed algorithms. We give the numerical experiments to show the efficiency and advantage of the proposed methods and we also used our proposed algorithm for solving the image deblurring and image recovery problems. Our result extends some related works in the literature and the primary experiments might also suggest their potential applicability. [ABSTRACT FROM AUTHOR]

The q‐rung orthopair fuzzy set (qROFS) defined by Yager is a generalization of Atanassov intuitionistic fuzzy set and Pythagorean fuzzy sets. In this paper, we define the knowledge measure for qROFS by using the tangent inverse function. This is the first approach to quantify the knowledge associated with qROFS. The membership and nonmembership functions as well as the hesitancy margin are used to define the knowledge measure which makes it capable of considering both knowledge and fuzziness. The entropy measure which is the dual of the knowledge measure is also defined. The properties of the proposed knowledge measure with graphical explanations are discussed. An application of the proposed knowledge measure in multiattribute group decision making problem under confidence level approach is given. [ABSTRACT FROM AUTHOR]

In intuitionistic fuzzy set and their generalizations such as Pythagorean fuzzy sets and q‐rung orthopair fuzzy sets, ranking is not easy to define. There are several techniques available in literature for ranking values in above mentioned orthopair fuzzy sets. It is interesting to see that almost all the proposed ranking methods produce distinct ranking. Notion of knowledge base is very important to study ranking proposed by different techniques. Aim of this paper is to critically analyze the available ranking techniques for q‐rung orthopair fuzzy values and propose a new graphical ranking method based on hesitancy index and entropy. Several numerical examples are tested with the proposed technique, which shows that the technique is intuitive and convenient for real life applications. [ABSTRACT FROM AUTHOR]

Summary: In this paper, we propose the modified splitting method for accretive operators in Banach space and prove some strong convergence theorems of the proposed method under suitable conditions. Our main results can be viewed as the improvement of the results of Takahashi et al. Indeed, we remove the conditions that limn→∞(rn−rn+1)=0 in our results. Moreover, we extend their results in Hilbert spaces to certain Banach spaces. Finally, we give some applications to the minimization problems with convergence analysis. [ABSTRACT FROM AUTHOR]

Current disquisition is expressed to elucidate the mathematical and engineering aspects of tangent hyperbolic liquid over a cone and plate which has valuable applications in industrial technological instruments such as cone and plate viscometer, spinning column technology, and biomass pyrolysis processing. The role of mixed convection and chemical reaction on physical features of fluid is considered. The attained coupled system is scrutinized by the aid of self-coded shooting method. In order to produce accuracy and refinement in the consequences, the coefficients of Runge–Kutta scheme are obliged. To get complete intellect about the current pagination, the impact of flow controlling variables on pertinent profiles are evaluated in quantitative and qualitative manner. The computations of wall drag force and heat and mass fluxes are presented pictorially and tabularly. From the thorough analysis, it is deduced that surface drag and convective thermal coefficient for cone is more in magnitude compared with those of plate. Similarly, dominance in thermal field is noted for cone compare with that in plate. Increment of velocity profile is revealed with enhancement in mixed convection parameter, whereas contrasting behavior is observed by varying Williamson and magnetic field parameters. Declining aptitude in thermal profile is exhibited against Prandtl number, whereas temperature of fluid mounts by changing the Brownian movement and thermophoresis parameters. [ABSTRACT FROM AUTHOR]

We presented the applications of entropy generation for SWCNTs and MWCNTs based on kerosene oil for Casson nanofluid flow by rotating channels. Kerosene oil has advanced thermal conductivity and exclusive features and has a lot of practical uses due to its unique behavior. That is why we have used kerosene oil as a based fluid. For the entropy generation second law of thermodynamics is applied and implemented for the nanofluid transport mechanism. In the presence of magnetic field, the effects of thermal radiations and heat source/sink on the temperature profiles are studied. The fluid flow is supposed in steady state. With the help of suitable similitude parameters, the leading equations have been transformed to a set of differential equations. The solution of the modeled problem has been carried out with the homotopic approach. The physical properties of carbon nanotubes are shown through tables. The effects of the imbedded physical parameters on the velocities, temperature, entropy generation rate, and Bejan number profiles are investigated and presented through graphs. Moreover, the impact of significant parameters on surface drag force and heat transfer rate is tabulated. [ABSTRACT FROM AUTHOR]

We prove some common fixed point results for two mappings satisfying generalized contractive condition in b-metric space. Note that b-metric of main results in this work are not necessarily continuous. So our results extend and improve several previous works. We also present one example that shows the applicability and usefulness of our results. [ABSTRACT FROM AUTHOR]

We approach the generalized Ulam-Hyers-Rassias (briefly, UHR) stability of quadratic functional equations via the extensive studies of fixed point theory. Our results are obtained in the framework of modular spaces whose modulars are lower semicontinuous (briefly, lsc) but do not satisfy any relatives of Δ2-conditions. [ABSTRACT FROM AUTHOR]

We point out some equivalence between the results in (Sedghi et al., 2012) and (Khamsi, 2010).Then, we introduce the notion of a general distance between three arbitrary points and study some of its properties. In the final section, some fixed point results are proposed. [ABSTRACT FROM AUTHOR]

We study and establish the existence of a solution for a generalized mixed equilibriumproblem with a bifunction defined on the dual space of a Banach space. Furthermore, we also modify Halpern-Mann iterations for finding a common solution of a generalized mixed equilibrium problem and a fixed point problem. Under suitable conditions of the purposed iterative sequences, the strong convergence theorems are established by using sunny generalized nonexpansive retraction in Banach spaces. Our results extend and improve various results existing in the current literature. [ABSTRACT FROM AUTHOR]

Two countable families of hemirelatively nonexpansive mappings are considered based on a hybrid projection algorithm. Strong convergence theorems of iterative sequences are obtained in an uniformly convex and uniformly smooth Banach space. As applications, convex feasibility problems, equilibrium problems, variational inequality problems, and zeros of maximal monotone operators are studied. [ABSTRACT FROM AUTHOR]

We introduce a new iterative algorithm for finding a common element of a fixed point problem of amenable semigroups of nonexpansive mappings, the set solutions of a system of a general system of generalized equilibria in a real Hilbert space. Then, we prove the strong convergence of the proposed iterative algorithm to a common element of the above three sets under some suitable conditions. As applications, at the end of the paper, we apply our results to find the minimum-norm solutions which solve some quadratic minimization problems. The results obtained in this paper extend and improve many recent ones announced by many others. [ABSTRACT FROM AUTHOR]

Recently, Samet et al. (2012) introduced the notion of α-ψ-contractive mappings and established some fixed point results in the setting of complete metric spaces. In this paper, we introduce the notion of weak α-ψ-contractive mappings and give fixed point results for this class of mappings in the setting of partial metric spaces. Also, we deduce fixed point results in ordered partial metric spaces. Our results extend and generalize the results of Samet et al. [ABSTRACT FROM AUTHOR]

We introduce a b-metric on the cone b-metric space and then prove some equivalences between them. As applications, we show that fixed point theorems on cone b-metric spaces can be obtained from fixed point theorems on b-metric spaces. [ABSTRACT FROM AUTHOR]

Recently, Basha (2011) established the best proximity point theorems for proximal contractions of the first and second kinds which are extension of Banach's contraction principle in the case of non-self-mappings. The aim of this paper is to extend and generalize the notions of proximal contractions of the first and second kinds which aremore general than the notion of self-contractions, establish the existence of an optimal approximate solution theorems for these non-self-mappings, and also give examples to validate ourmain results. [ABSTRACT FROM AUTHOR]

Ran and Reurings (2004) established an interesting analogue of Banach Contraction Principle in a completemetric space equipped with a partial ordering and also utilized the same oneto discuss the existence of solutions to matrix equations. Motivated by this paper, we prove results on coincidence points for a pair of weakly increasingmappings satisfying a nonlinear contraction condition described by a rational expression on an ordered complete metric space. The uniqueness of common fixed point is also discussed. Some examples are furnished to demonstrate the validity of the hypotheses of our results. As an application, we derive an existence theorem for the solution of an integral equation. [ABSTRACT FROM AUTHOR]

We propose new iterative schemes for finding the common element of the set of common fixed points of countable family of nonexpansive mappings, the set of solutions of the variational inequality problem for relaxed cocoercive and Lipschitz continuous, the set of solutions of system of variational inclusions problem, and the set of solutions of equilibrium problems in a real Hilbert space by using the viscosity approximation method. We prove strong convergence theorem under some parameters. The results in this paper unify and generalize some well-known results in the literature. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce the modified Halpern-type iterative method by the generalized f -projection operator for finding a common solution of fixed-point problem of a totally quasi-f-asymptotically nonexpansive mapping and a system of equilibrium problems in a uniform smooth and strictly convex Banach space with the Kadec-Klee property. Consequently, we prove the strong convergence for a common solution of above two sets. Our result presented in this paper generalize and improve the result of Chang et al., (2012), and some others. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce a new iterative scheme for finding a common element of the set of solutions of generalized mixed equilibrium problems, the set of solutions of variational inequality problems, the zero point of maximal monotone operators, and the set of two countable families of quasi-f-nonexpansive mappings in Banach spaces. Moreover, the strong convergence theorems of this method are established under the suitable conditions of the parameter imposed on the algorithm. Finally, we apply our results to finding a zero point of inverse-strongly monotone operators and complementarity problems. Our results presented in this paper improve and extend the recently results by many others. [ABSTRACT FROM AUTHOR]

We introduce a new iterative algorithm for solving a common solution of the set of solutions of fixed point for an infinite family of nonexpansive mappings, the set of solution of a system of mixed equilibrium problems, and the set of solutions of the variational inclusion for a ß-inversestrongly monotone mapping in a real Hilbert space. We prove that the sequence converges strongly to a common element of the above three sets under some mild conditions. Furthermore, we give a numerical example which supports our main theorem in the last part. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study the existence and convergence analysis of the solutions of the system of mixed variational inequalities in Banach spaces by using the generalized f projection operator. The results presented in this paper improve and extend important recent results of Zhang et al. (2011) and Wu and Huang (2007) and some recent results. [ABSTRACT FROM AUTHOR]

We introduce an iterative algorithm for finding a common element of the set of solutions of a system of mixed equilibrium problems, the set of solutions of a general system of variational inequalities for Lipschitz continuous and relaxed cocoercive mappings, the set of common fixed points for nonexpansive semigroups, and the set of common fixed points for an infinite family of strictly pseudocontractive mappings in Hilbert spaces. Furthermore, we prove a strong convergence theorem of the iterative sequence generated by the proposed iterative algorithm under some suitable conditions which solves some optimization problems. Our results extend and improve the recent results of Chang et al. (2010) and many others. [ABSTRACT FROM AUTHOR]

The propose of this paper is to present a modified block iterative algorithm for finding a common element between the set of solutions of the fixed points of two countable families of asymptotically relatively nonexpansive mappings and the set of solution of the system of generalized mixed equilibrium problems in a uniformly smooth and uniformly convex Banach space. Our results extend many known recent results in the literature. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce a new iterative scheme for finding common solutions of the variational inequalities for an inverse strongly accretive mapping and the solutions of fixed point problems for nonexpansive semigroups by using the modified viscosity approximation method associate with Meir-Keeler type mappings and obtain some strong convergence theorem in a Banach spaces under some parameters controlling conditions. Our results extend and improve the recent results of Li and Gu 2010(, Wangkeeree and Preechasilp 2012(, Yao and Maruster 2011(, and many others. [ABSTRACT FROM AUTHOR]

This paper deals with new methods for approximating a solution to the fixed point problem; find x ∈ F(T), where H is a Hilbert space, C is a closed convex subset of H, f is a ρ-contraction from C into H, 0 < ρ < 1, A is a strongly positive linear-bounded operator with coefficient γ > 0, 0 < γ < γ/ρ, T is a nonexpansive mapping on C, and PF(T) denotes the metric projection on the set of fixed point of T.Under a suitable different parameter, we obtain strong convergence theorems by using the projection method which solves the variational inequality 〈(A-γf)x+τ(I-S)x, x- x) = 0 for x ∈ F(T), where τ ∈ [0,∞). Our results generalize and improve the corresponding results of Yao et al. (2010) and some authors. Furthermore, we give an example which supports our main theorem in the last part. [ABSTRACT FROM AUTHOR]

We introduce a general implicit iterative scheme base on viscosity approximation method with a f-strongly pseudocontractive mapping for finding a common element of the set of solutions for a system of mixed equilibrium problems, the set of common fixed point for a nonexpansive semigroup, and the set of solutions of system of variational inclusions with set-valued maximal monotone mapping and Lipschitzian relaxed cocoercive mappings in Hilbert spaces. Furthermore, we prove that the proposed iterative algorithm converges strongly to a common element of the above three sets, which is a solution of the optimization problem related to a strongly positive bounded linear operator [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce and study a modified Halpern's iterative scheme for solving the split feasibility problem (SFP) in the setting of infinite-dimensional Hilbert spaces. Under suitable conditions a strong convergence theorem is established. The main result presented in this paper improves and extends some recent results done by Xu (Iterative methods for the split feasibility problem in infinite-dimensional Hilbert space, Inverse Problem 26 (2010) 105018) and some others. [ABSTRACT FROM AUTHOR]

This paper discusses the monotone variational inequality over the solution set of the variational inequality problem and the fixed point set of a nonexpansive mapping. The strong convergence theorem for the proposed algorithm to the solution is guaranteed under some suitable assumptions. [ABSTRACT FROM AUTHOR]

We introduce a new general system of generalized nonlinear mixed composite-type equilibria and propose a new iterative scheme for finding a common element of the set of solutions of a generalized equilibrium problem, the set of solutions of a general system of generalized nonlinear mixed composite-type equilibria, and the set of fixed points of a countable family of strict pseudocontraction mappings. Furthermore, we prove the strong convergence theorem of the purposed iterative scheme in a real Hilbert space. As applications, we apply our results to solve a certain minimization problem related to a strongly positive bounded linear operator. Finally, we also give a numerical example which supports our results. The results obtained in this paper extend the recent ones announced by many others. [ABSTRACT FROM AUTHOR]

We introduce a new iterative algorithm for finding a common element of the set of solutions of a system of generalized mixed equilibrium problems, zero set of the sum of a maximal monotone operators and inverse-strongly monotone mappings, and the set of common fixed points of an infinite family of nonexpansive mappings with infinite real number. Furthermore, we prove under some mild conditions that the proposed iterative algorithm converges strongly to a common element of the above four sets, which is a solution of the optimization problem related to a strongly positive bounded linear operator. The results presented in the paper improve and extend the recent ones announced by many others. [ABSTRACT FROM AUTHOR]

We generalized the notion of proximal contractions of the first and the second kinds and established the best proximity point theorems for these classes. Our results improve and extend recent result of Sadiq Basha (2011) and some authors. [ABSTRACT FROM AUTHOR]

We give some initial properties of a subset of modular metric spaces and introduce some fixedpoint theorems for multivalued mappings under the setting of contraction type. An appropriate example is as well provided. The stability of fixed points in our main theorems is also studied. [ABSTRACT FROM AUTHOR]

We introduce an implicit-relation-type cyclic contractive condition for a map in a metric space and derive existence and uniqueness results of fixed points for such mappings. Examples are given to support the usability of our results. At the end of the paper, an application to the study of existence and uniqueness of solutions for a class of nonlinear integral equations is presented. [ABSTRACT FROM AUTHOR]

We extend the recent results of the coupled fixed point theorems of Cho et al. (2012) by weakening the concept of the mixed monotone property. We also give some examples of a nonlinear contraction mapping, which is not applied to the existence of the coupled fixed point by the results of Cho et al. but can be applied to our results. The main results extend and unify the results of Cho et al. and many results of the coupled fixed point theorems. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to consider a modified hybrid steepest-descent method by using a viscosity approximation method with a weakly contractive mapping for finding the common element of the set of a common fixed point for an infinite family of nonexpansive mappings and the set of solutions of a system of an equilibrium problem. The sequence is generated from an arbitrary initial point which converges in norm to the unique solution of the variational inequality under some suitable conditions in a real Hilbert space. The results presented in this paper generalize and improve the results of Moudafi (2000), Marino and Xu (2006), Tian (2010), Saeidi (2010), and some others. Finally, we give an application to minimization problems and a numerical example which support our main theorem in the last part. [ABSTRACT FROM AUTHOR]

We prove new fixed point and common fixed point theorems for generalized weak contractive mappings of integral type in modular spaces. Our results extend and generalize the results of A. Razani and R. Moradi (2009) and M. Beygmohammadi and A. Razani (2010). [ABSTRACT FROM AUTHOR]

We introduce a new general iterative method for finding a common element of the set of solutions of fixed point for nonexpansive mappings, the set of solution of generalized mixed equilibrium problems, and the set of solutions of the variational inclusion for a β-inverse-strongly monotone mapping in a real Hilbert space. We prove that the sequence converges strongly to a common element of the above three sets under some mild conditions. Our results improve and extend the corresponding results of Marino and Xu (2006), Su et al. (2008), Klin-eam and Suantai (2009), Tan and Chang (2011), and some other authors. [ABSTRACT FROM AUTHOR]

We introduce a new general composite iterative scheme for finding a common fixed point of nonexpansive semigroups in the framework of Banach spaces which admit a weakly continuous duality mapping. A strong convergence theorem of the purposed iterative approximation method is established under some certain control conditions. Our results improve and extend announced by many others. [ABSTRACT FROM AUTHOR]

We prove strong and weak convergence theorems of modified hybrid proximal-point algorithms for finding a common element of the zero point of a maximal monotone operator, the set of solutions of equilibrium problems, and the set of solution of the variational inequality operators of an inverse strongly monotone in a Banach space under different conditions. Moreover, applications to complementarity problems are given. Our results modify and improve the recently announced ones by Li and Song (2008) and many authors. [ABSTRACT FROM AUTHOR]

We introduce a new iterative scheme by shrinking projection method for finding a common element of the set of solutions of generalized mixed equilibrium problems, the set of common solutions of variational inclusion problems with set-valued maximal monotone mappings and inverse-strongly monotone mappings, the set of solutions of fixed points for nonexpansive semigroups, and the set of common fixed points for an infinite family of strictly pseudocontractive mappings in a real Hilbert space. We prove that the sequence converges strongly to a common element of the above four sets under some mind conditions. Furthermore, by using the above result, an iterative algorithm for solution of an optimization problem was obtained. Our results improve and extend the corresponding results of Martinez-Yanes and Xu (2006), Shehu (2011), Zhang et al. (2008), and many authors. [ABSTRACT FROM AUTHOR]

We introduce a new general system of variational inclusions in Banach spaces and propose a new iterative scheme for finding common element of the set of solutions of the variational inclusion with set-valued maximal monotone mapping and Lipschitzian relaxed cocoercive mapping and the set of fixed point of nonexpansive semigroups in a uniformly convex and 2-uniformly smooth Banach space. Furthermore, strong convergence theorems are established under some certain control conditions. As applications, finding a common solution for a system of variational inequality problems and minimization problems is given. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to present a new hybrid block iterative scheme by the generalized f - projection method for finding a common element of the fixed point set for a countable family of uniformly quasi-Φ-asymptotically nonexpansive mappings and the set of solutions of the system of generalized mixed equilibrium problems in a strictly convex and uniformly smooth Banach space with the Kadec-Klee property. Furthermore, we prove that our new iterative scheme converges strongly to a common element of the aforementioned sets. The results presented in this paper improve and extend important recent results in the literature. [ABSTRACT FROM AUTHOR]

We introduce a new general hybrid iterative algorithm for finding a common element of the set of solution of fixed point for a nonexpansive mapping, the set of solution of generalized mixed equilibrium problem, and the set of solution of the variational inclusion for a β-inverse-strongly monotone mapping in a real Hilbert space. We prove that the sequence converges strongly to a common element of the above three sets under some mild conditions. Our results improve and extend the corresponding results of Marino and Xu (2006), Yao and Liou (2010), Tan and Chang (2011), and other authors. [ABSTRACT FROM AUTHOR]

We introduce a new modified Ishikawa iterative process and a new W-mapping for computing fixed points of an infinite family of strict pseudo contractions mapping in the framework of q-uniformly smooth Banach spaces. Then, we establish the strong convergence theorem of the proposed iterative scheme under some mild conditions. The results obtained in this paper extend and improve the recent results of Cai and Hu 2010, Dong et al. 2010, Katchang and Kumam 2011 and many others in the literature. [ABSTRACT FROM AUTHOR]

We introduce a general composite iterative scheme for nonexpansive semigroups in Banach spaces. We establish some strong convergence theorems of the general iteration scheme under different control conditions. The results presented in this paper improve and extend the corresponding results of Marino and Xu (2006), and others, from Hilbert spaces to Banach spaces. [ABSTRACT FROM AUTHOR]