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Using the Mann method and the shrinking projection method, we present generalized forms of iterative scheme generating methods and compared them with prior frameworks. To this end, the properties of mean-valued sequences are leveraged. Subsequently, we establish a convergence theorem similar to that developed by Martinez-Yanes and Xu. This approach highlights the difference between the conventional shrinking projection method and the Martinez-Yanes and Xu variant. The proposed frameworks yield various types of iterative schemes for finding common fixed points, including a three-step iterative scheme. The class of mappings considered incorporate general types, including nonexpansive mappings. [ABSTRACT FROM AUTHOR]

In this manuscript, we introduce a new class of uniformly L-Lipschitzian and total asymptotically quasi-nonexpansive mappings, which is significantly more general than many known nonexpansive mappings that appeared before. We establish some convergence and Δ-convergence theorems for two infinite families of such mappings in the setting of CAT(κ) spaces. Our results refine, generalize, and improve several corresponding results in the existing literature. [ABSTRACT FROM AUTHOR]

In this paper, we prove some fixed point results for a pair of relatively nonexpansive mappings using Thakur iteration in uniformly convex W-hyperbolic spaces. Our results extend some of the existing results in the literature. We illustrate the results with an example. Also, we compare the convergence of two different types of Thakur iterations for a pair of relatively nonexpansive mappings and establish that one converges faster than the other. We also establish the existence of a best proximity pair using the main theorem. [ABSTRACT FROM AUTHOR]

In this paper, we prove the existence and uniqueness of common fixed point of tower type contractive mappings in complete metric (pseudo)modular spaces involving the theoretic relation. However, the newly introduced contraction in this paper further characterize and includes in their full strength several existing results in metrical fixed point theory. Some nontrivial supportive examples were given to justify our result. Our results generalize, improve, and unify some existing results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce two new classes of mixed (S,T)-α-admissible mappings and interspersed (S, g,T)-α-admissible mappings and study the sufficient conditions for the existence and uniqueness of a common fixed point of generalized (αs, ξ, ħ, τ)-Geraghty contractive mapping in the framework of partial b-metric spaces. We also provide two examples to show the applicability and validity of our results. Moreover, we present an application to the existence of solutions to an integral equation by means of one of our results. [ABSTRACT FROM AUTHOR]

Abstract In this manuscript, we introduce a new class of uniformly L-Lipschitzian and total asymptotically quasi-nonexpansive mappings, which is significantly more general than many known nonexpansive mappings that appeared before. We establish some convergence and Δ-convergence theorems for two infinite families of such mappings in the setting of CAT(κ) spaces. Our results refine, generalize, and improve several corresponding results in the existing literature.

In this paper, we introduce two new classes of mixed $ (\mathcal{S, T}) $-$ \alpha $-admissible mappings and interspersed $ (\mathcal{S}, \mathfrak{g}, \mathcal{T}) $-$ \alpha $-admissible mappings and study the sufficient conditions for the existence and uniqueness of a common fixed point of generalized $ (\alpha_s, \xi, \hbar, \tau) $-Geraghty contractive mapping in the framework of partial $ b $-metric spaces. We also provide two examples to show the applicability and validity of our results. Moreover, we present an application to the existence of solutions to an integral equation by means of one of our results.

In this research, we studied modified inertial composite subgradient extragradient implicit rules for finding solutions of a system of generalized equilibrium problems with a common fixed-point problem and pseudomonotone variational inequality constraints. The suggested methods consisted of an inertial iterative algorithm, a hybrid deepest-descent technique, and a subgradient extragradient method. We proved that the constructed algorithms converge to a solution of the considered problem, which also solved some hierarchical variational inequality.

Motivated by Gopal and Vetro, we introduce a symmetric pair of β-admissible mappings and obtain common fixed point theorems for such a pair in complete and weak G-complete fuzzy metric spaces. In particular, we rectified, generalize and improve the common fixed point theorem obtained by Turkoglu and Sangurlu for two fuzzy ψ-contractive mappings. We include non-trivial examples to exhibit the generality and demonstrate our results.

Abstract In this article, we prove new common fixed-point theorems on a C ∗ $\mathscr{C}^{*}$ -algebra-valued R $\mathcal{R}$ -metric space. An example is given based on our obtained results. To enhance our results, a strong application based on the fractional-order initial value problem is provided.

In this paper, we study the generalized F-iterated function system in G-metric space. Several results of common attractors of generalized iterated function systems obtained by using generalized F-Hutchinson operators are also established. We prove that the triplet of F-Hutchinson operators defined for a finite number of general contractive mappings on a complete G-metric space is itself a generalized F-contraction mapping on a space of compact sets. We also present several examples in 2-D and 3-D for our results. [ABSTRACT FROM AUTHOR]

This paper investigates the existence of common fixed points for mappings satisfying generalized rational type contractive conditions in the framework of bicomplex valued metric spaces. Our findings extend well-established results in the existing literature. As an application of our leading result, we explore the existence and uniqueness of solutions of the Volttera integral equation of the second kind. [ABSTRACT FROM AUTHOR]

This study aims to establish common fixed point theorems for a pair of compatible self-mappings within the framework of extended parametric  S b -metric spaces. To support our assertions, we provide corollaries and examples accompanied with graphical representations. Moreover, we leverage our principal outcome to guarantee the existence of a common solution to a system of integral equations. [ABSTRACT FROM AUTHOR]

For solving a common fixed point of a finite family of G-nonexpansive mappings, we propose a parallel inertial SP-iteration monotone hybrid algorithm (PISPMHA). Weak convergence theorem is established for PISPMHA in Hilbert spaces endowed with graphs. Convergence behavior of PISPMHA is analyzed and discussed. As applications, we apply PISPMHA to solve linear system, differential, and signal recovery problems. [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]

Recent studies have highlighted fixed point theorems in the context of bicomplex valued metric spaces, utilizing rational type contractions with coefficients defined by two-variable control functions. In our research, we extend these findings by proposing new theorems for identifying common fixed points within bicomplex valued metric spaces, employing rational type contractions characterized by three-variable control functions as coefficients. We have refined the contraction conditions presented in numerous existing theorems by substituting constants with a limited number of control functions for more versatility in bicomplex valued metric spaces. This advancement broadens the scope of several significant findings in the literature. To demonstrate the efficacy of our results, we offer compelling examples that validate our theorems. Furthermore, we apply our primary findings to effectively address the Urysohn integral equation system, showcasing the practical application of our research. [ABSTRACT FROM AUTHOR]

This paper is the first to introduce a fixed point problem of integral type in a -metric space. We study sufficient conditions for the existence and uniqueness of a common fixed point of contractive mappings of integral type. We also give two examples to support our results. [ABSTRACT FROM AUTHOR]

In this paper, we obtain an equivalent condition to the existence of a common fixed point of a given family of nonexpansive mappings defined on a Hadamard space. Moreover, if the space is bounded, we show that the generating process of the approximate sequence by a specific projection method will stop in finite steps if there is no common fixed point. It is a significant advantage to reveal the nonexistence of a common fixed point in a finite time. [ABSTRACT FROM AUTHOR]

In this paper we establish the existence of a common fixed point from a pair of setvalued mappings. By utilizing the concept of convergence of set-valued mappings’ sequences, both ordinary and pointwise convergence, we establish a common fixed point theorem. This our newly result is a generalization of common fixed point theorem of set-valued mappings on partial metric spaces. Further, we establish newly common fixed point theorem under ϕ-contraction on partial metric spaces. [ABSTRACT FROM AUTHOR]

In this article, we prove new common fixed-point theorems on a C ∗ -algebra-valued R -metric space. An example is given based on our obtained results. To enhance our results, a strong application based on the fractional-order initial value problem is provided. [ABSTRACT FROM AUTHOR]

In this work, we study a parallel viscosity extragradient method for approximating a common solution of a finite system of pseudomonotone equilibrium problems and common fixed point problem for nonexpansive mappings in Hadamard spaces. We propose an iterative method and prove its strong convergence to an element in the intersection of the solution set of finite system of equilibrium problems and the fixed points set of nonexpansive mappings. Furthermore, we give an example in a Hadamard space which is not an Hilbert space to support the convergence theorem in the paper. This result generalizes and extends recent results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, by taking ${{\mathcal C}_\mathcal{A}}-$simulation function and Proinov type function into account, we set up a new contraction mapping called Suzuki$-$Proinov $\mathpzc{Z^*}_{\aE^*}^{\aR}(\alpha)-$contraction, including both rational expressions that possess quadratic terms and $\aE-$type contractions. Furthermore, we demonstrate a common fixed point theorem through the mappings endowed with triangular $\alpha-$admissibility in the setting of modular $b-$metric spaces. Besides that, we achieve some new outcomes that contribute to the current ones in the literature through the main theorem, and, as an application, we examine the existence of solutions to a class of functional equations emerging in dynamic programming.

In this article, we establish some common fixed point theorems in the setting of bounded metric spaces without using neither the compactness nor the uniform convexity of the space. Some examples are built to show the superiority of the obtained results compared to the existing ones in the literature. Moreover, we apply the main result to show the existence and uniqueness of a solution for a nonlinear integral system.

The concept of b-metric-like space is a generalization of the notions of partial metric space, metric-like space and b-metric space. In the present paper, we establish the existence and uniqueness of common fixed points in a b-metric-like space. Then we derive some common fixed point results in partial metric spaces, metric-like spaces, and b-metric spaces. [ABSTRACT FROM AUTHOR]

In this paper, we derive coincidence point and common fixed point results under order homotopies of families of mappings in partially ordered b -metric spaces. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a three-step iterative scheme, called the MF-iteration process to approximate a common fixed point for a hybrid pair {τ, T} of single-valued and multi-valued maps satisfying a generalized contractive condition defined on uniformly convex Banach spaces. We establish the strong convergence theorem for the proposed process under some basic boundary conditions. We give a numerical example to prove our results’ convergence rate. Further, we compare the convergence speed of Sokhuma and Kaewkhao [29] and MF-iterations. we show numerically that the considered iterative scheme converges faster than Sokhuma and Kaewkhao [29] for single-valued and multi-valued non-expansive mappings. Our newly proven results generalize several relevant results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, by taking CA -simulation function and Proinov type function into account, we set up a new contraction mapping called Suzuki-Proinov Z*RE* (a)-contraction, including both rational expressions that possess quadratic terms and E-type contractions. Furthermore, we demonstrate a common fixed point theorem through the mappings endowed with triangular a-admissibility in the setting of modular b-metric spaces. Besides that, we achieve some new outcomes that contribute to the current ones in the literature through the main theorem, and, as an application, we examine the existence of solutions to a class of functional equations emerging in dynamic programming. [ABSTRACT FROM AUTHOR]

The study delves into multiplicative contractions, exploring the existence and uniqueness of common fixed points for a weakly compatible pair of mappings. Those mappings adhere to specific multiplicative contraction conditions characterized by exponents expressed as fraction multiplicative metric spaces. It is noted that a metric can induce a multiplicative metric, and conversely, a multiplicative metric can give a rise to a metric on a nonempty set. As an application, another proof of the existence and uniqueness of the solution of a multiplicative initial problem is given. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to demonstrate common fixed point theorems in intuitionistic Mengerspace. In our main result we use the notion of CLR property for type (K) Compatible mappings. The importance of CLR property is that subspaces need not be closed for the survival of fixed points. Many authors utilize the concept of CLR property to prove theorems on fixed point in intuitionistic Mengerspaces for various type of compatible mappings.The results thus obtained, generalizes and extends some known results in intuitionistic menger space. [ABSTRACT FROM AUTHOR]

Motivated by Gopal and Vetro, we introduce a symmetric pair of β-admissible mappings and obtain common fixed point theorems for such a pair in complete and weak G-complete fuzzy metric spaces. In particular, we rectify, generalize and improve the common fixed point theorem obtained by Turkoglu and Sangurlu for two fuzzy Ψ-contractive mappings. We include non-trivial examples to exhibit the generality and demonstrate our results. [ABSTRACT FROM AUTHOR]

In this paper, we establish strong convergence of the Halpern's type iteration for a semigroup of α-nonexpansive mappings in Banach spaces. Using the concept of quasilinearization, we extend this result to CAT(0) spaces, an important subclass of metric spaces. Our work generalizes and complements several comparable results existing in the literature. [ABSTRACT FROM AUTHOR]

In this work, we prove in a partial b-metric space a common fixed point theorem for two pairs of mappings that satisfy a generalized contraction condition which involves a simulation function . Our result generalizes and extends several results from the existing literature. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce the notion of (α,β)-Zb-Geraghty type contraction via b-simulation function and use this contraction to establish a common fixed point theorem for a pair of self-mappings in the context of a b-metric-like space. Our result extends and generalizes the result of Matthews [21], Khojasteh et al. [20], Demma et al. [15], Chandok [12] and some others also. We deduce some corollaries from our main result and provide examples to illustrate our results. Moreover, we apply our result to obtain a solution of second order differential equation. [ABSTRACT FROM AUTHOR]

The main aim of our manuscript is to present common fixed point solution for Urysohn integral equation 41, Our paper divided in to two folds, Firstly with the help of class function we established fixed point results for two pair of weakly compatible mapping satisfying the contractive condition of rational type in CVMS our work inspired from [15]. Secondly Common solution to the integral equation, .... [ABSTRACT FROM AUTHOR]

It is well-known that the fixed point theory plays a very important role in theory and applications. In 2017, Choi et al. [4] introduced the notion of bicomplex valued metric spaces (bi-CVMS) and established common fixed point results for weakly compatible mappings. On the other hand, in 1942, K. Menger [14] initiated the study of probabilistic metric spaces where he replaced the distance function d(x, y) by distribution function Fx, y(t), where the value of Fx, y(t) is interpreted as the probability that the distance between x and y be less than t, t > 0. In this paper, we have used bicomplex-valued metric on a set. We have taken Fx, y(t) as the probability that norm of the distance between x and y be less than t, i.e., ||d(x, y)|| < t, t > 0 and initiated menger space with bicomplex valued metric. We also aim to prove certain common fixed point theorems for a pair of weakly compatible mappings satisfying (CLRg) or (E.A) property in this space. [ABSTRACT FROM AUTHOR]

In this article, we introduce and study some strong convergence theorems for a mixed-type SP-iteration for three asymptotically nonexpansive self-mappings and three asymptotically nonexpansive nonself-mappings in uniformly convex hyperbolic spaces. In addition to that, we provide an illustrative example. The findings here expand and improve upon some of the relevant conclusions found in the published literature.

In this paper, we prove the existence and uniqueness of common fixed point of tower type contractive mappings in complete metric (pseudo)modular spaces involving the theoretic relation. However, the newly introduced contraction in this paper further characterize and includes in their full strength several existing results in metrical fixed point theory. Some nontrivial supportive examples were given to justify our result. Our results generalize, improve, and unify some existing results.

The aim of the present research work is to investigate the solution of Urysohn integral equation by common fixed point result in the setting of complex valued b-metric space. To obtain the objective, we used a generalized rational contraction involving control functions and a pair of self-mappings. In this way, we generalize some well-known results of literature. Some non-trivial examples are also flourished to demonstrate the innovation of our principal result. [ABSTRACT FROM AUTHOR]

In this article, some common fixed point theorems were proved in complete 2- metric space using weakly compatible mappings in which property (E.A), common property (E.A) and (E.A) like Property are involved. [ABSTRACT FROM AUTHOR]

In this paper, we present the generalized iterated function system for the construction of common fractals of generalized contractive mappings in the setup of dislocated metric spaces. The well-posedness of attractors' problems of rational contraction maps in the framework of dislocated metric spaces is also established. Moreover, the generalized collage theorem is also obtained in dislocated metric spaces. [ABSTRACT FROM AUTHOR]

The purpose of this article is to extend Banach's contraction principle through a new rational expression in the contractive condition to establish the existence and uniqueness of fixed point of a closed subset of Hilbert space to a self mapping. The result is extended to a pair of self mappings and positive integers powers of a pair mapping and further extended to a sequence of mappings in the space. The presented results extend and generalized various known comparable results from the current literature. [ABSTRACT FROM AUTHOR]

In this paper, it is our purpose to introduce an inertial-like algorithm for approximating common fixed points of continuous pseudocontractive mappings in the framework of real Hilbert spaces. We prove strong convergence theorems for the sequence generated by the algorithm under certain conditions on the control sequences. We also provide numerical examples to demonstrate the efficiency of our algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we define the new concept of E f , g -contraction mapping and check common fixed point theorems for such contractions in metrically convex metric spaces. We provide an example to support the presented results. [ABSTRACT FROM AUTHOR]

We introduce a C' iric' type contraction principle in a vector-valued b-metric space that generalizes Perov's contraction principle. We investigate the possible conditions on the mappings W, E: G → G (G is a non-empty set), for which these mappings admit a unique common fixed point in G subject to a nonlinear operator F: Pm → Rm. We illustrate the hypothesis of our findings with examples. We consider an infectious disease model represented by the system of delay integrodifferential equations and apply the obtained fixed point theorem to show the existence of a solution to this model. [ABSTRACT FROM AUTHOR]

In this work, we define a new notion of μ F -contraction in Banach spaces, by modeling with measure of non-compactness the well-known concept of F -contraction given by Wardowski in metric spaces. We prove a fixed-point theorem and a common fixed-point theorem for our contraction. Our results extend the well-known Darbo contraction principle and large contractions in the literature. Furthermore, the paper contains examples and applications that show the validity of our results. [ABSTRACT FROM AUTHOR]

We consider an iterative scheme to approximate common fixed points of a pair of single and multi-valued mappings satisfying the socalled condition (Cα) in Banach spaces. We also compare its rate of convergence with some existing iterative schemes. We show that our iterative scheme converges faster than these schemes. It has been confirmed numerically and depicted graphically. We prove the convergence results for our proposed scheme. We also provide an application of our iterative scheme to solve the Split Common Fixed Point (SCFP) Problem. [ABSTRACT FROM AUTHOR]

The aim of the present research article is to solve the system of linear equations using common fixed point theorems in the context of bicomplex valued metric spaces. To obtain our main objective, we introduce generalized contractive conditions in bicomplex valued metric spaces and establish common fixed point theorems for self mappings. We also give a significant example to demonstrate the legitimacy of the given theorems. [ABSTRACT FROM AUTHOR]