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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 establish a strong convergence theorem that approximates a common fixed point of two nonlinear mappings by comprehensively using an Ishikawa iterative method, a hybrid method, and a mean-valued iterative method. The shrinking projection method is also developed. The nonlinear mappings are a general type that includes nonexpansive mappings and other classes of well-known mappings. The two mappings are not assumed to be continuous or commutative. The main theorems in this paper generate a variety of strong convergence theorems including a type of "three-step iterative method". An application to the variational inequality problem is also given. [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 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]

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]

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]

In this paper, we prove some common fixed point theorems in S-metric spaces for a pair of weakly compatible self-mappings using control function and give some consequences of the established result. We also furnish some examples to demonstrate the validity of the results. The results presented in this paper generalize, extend and enrich several results in the existing literature. [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, 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, 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]

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 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 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 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]

This paper reports a modified F-iterative process for finding the fixed points of three generalized ff-nonexpansive mappings. We assume certain assumptions to establish the weak and strong convergence of the scheme in the context of a Banach space. We suggest a numerical example of generalized ff-nonexpansive mappings which exceeds, properly, the category of functions furnished with a condition (C). After that, we show that our modified F-iterative scheme of this example converges to a common fixed point of three generalized ff-nonexpansive mappings. As an application of our main findings, we suggest a new projection-type iterative scheme to solve variational inequality problems in the setting of generalized ff-nonexpansive mappings. The main finding of the paper is new and extends many known results of the literature. [ABSTRACT FROM AUTHOR]

In this paper, we prove some common fixed point theorems on S-metric spaces for two pairs of weakly compatible mappings by using C-class functions and give some consequences as corollaries of the established results. We also give an example in support of the result. The results presented in this paper generalize, extend and enrich various results in the existing literature. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to prove some common fixed point theorems for two pairs of self-mappings satisfying (CLR)-property and some Φ-type contractive condition in the framework of S-metric spaces. We also give some examples to validate the results. The results presented in this paper generalize, extend and unify several previous results in the existing literature. [ABSTRACT FROM AUTHOR]

In this paper, we present a modified SP iteration with the inertial technical term for three quasi-nonexpansive multivalued mappings in a Hilbert space. We then obtain weak convergence theorem under suitable conditions. The strong convergence theorems are given using CQ and shrinking projection methods with our modified iteration. Finally, we test some numerical experiments to illustrate that our inertial forward–backward method with the inertial technique term has a more effective convergence than that of the standard forward–backward method and Halpern algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we derive the coincidence fixed-point and common fixed-point results for ℑ-type mappings satisfying certain contractive conditions and containing fewer conditions imposed on function ℑ with regard to generalized metric spaces (in terms of Jleli Samet). Finally, a fractional boundary value problem is reduced to an equivalent Volterra integral equation, and the existence results of common solutions are obtained with the use of proved fixed-point results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate two Mann-type accelerated projection procedures with line search method for solving the pseudomonotone variational inequality (VIP) and the common fixedpoint problem (CFPP) of finitely many Bregman relatively nonexpansive mappings and a Bregman relatively asymptotically nonexpansive mapping in p-uniformly convex and uniformly smooth Banach spaces. Under mild conditions, we show weak and strong convergence of the proposed algorithms to a common solution of the VIP and CFPP, respectively. [ABSTRACT FROM AUTHOR]

In this paper, common fixed-point problems for locally contractive mappings in symmetric Gd-metric like spaces are proved and error bounds are disscussed in detail. Besides, we gave examples to validate main results. In our research, we have proved that a pair of self-mappings satisfies Banach contraction, in local domain instead of global domain. Also, application of Gd-metric like spaces for solving Urysohn integral equations is given. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to establish weak and strong convergence theorems of new three-step iterations for Iasymptotically nonexpansive mappings in Banach space.Also we introduce and study convergence theorems of the three-step iterative sequence for three I-asymptotically nonexpansive mappings in an uniformly convex Banach space. The results obtained in this paper extend and improve the recent ones announced by Chen and Guo [1], S. Temir [14], Yao and Noor[16] and many others. [ABSTRACT FROM AUTHOR]

It is meaningful and valuable to find common fixed points of different nonexpansive-type operators, which are associated with variational inequalities, integral equations, image process and other optimization problems in real life. The purpose of this paper is to suggest and consider a class of general semi-implicit iterative methods involving semi-implicit rule and inaccurate computing errors, which extend the iterative algorithm introduced by Ali et al. in 2020. Using Liu’s lemma, we analyze convergence and stability of the new iterative approximations for common fixed points of three different nonexpansive-type operators. Furthermore, we provide convergence rates of the new iterations and some numerical examples to illustrate the efficiency and stability of the new iterative schemes. As an application of our main results presented in this paper, we use the proposed iterative schemes to solve the known Stampacchia variational inequality. [ABSTRACT FROM AUTHOR]

In this paper, by means of a mapping φ ∈ Φ (P , P 1) , some new common fixed and coincidence point theorems for four and six nonlinear self-mappings in cone b -metric spaces are established, respectively. Also, some examples are given to prove the effectiveness of our results. And with some remarks stating that our results complement and sharply improve some related results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we establish a result for the existence of common fixed points for multi-valued mappings, satisfying some contractions for complex-valued b-metric spaces. Finally, we present an example to illustrate and support our results. [ABSTRACT FROM AUTHOR]

In the present paper, we prove common fixed point theorems under different contractive mappings on C ★ -algebra-valued bipolar metric spaces. The results generalize and expand some well-known results from the literature. Examples and applications are given to strengthen our conclusion. Additionally, as an application of our results, we show that some classes of the nonlinear fractional differential equations with the boundary conditions have a unique common solution. [ABSTRACT FROM AUTHOR]

In this paper, an a-complete extended Branciari b-distance space and rational α -- λ -- JS contractive conditions in the underlying spaces are introduced. Further, we establish the coincidence point, common fixed points, and uniqueness of fixed points for two pairs of mappings in new spaces under the aforementioned contractive conditions. We illustrate the work with an example and apply the results to determine the existence of solutions for a system of Urysohn integral equations. [ABSTRACT FROM AUTHOR]

In this paper, we present some results on the existence and uniqueness of common fixed points on d * -complete topological spaces. Our results generalize and improve upon earlier results in the literature. Finally, we give some examples in l p spaces, (p ∈ (0 , 1)) , where we use the obtained results. [ABSTRACT FROM AUTHOR]

The aim of this paper is to establish some common fixed point theorems for four self-mappings satisfying (E.A) and weak compatible properties and contractive type condition involving rational expressions in the setting of complex valued S-metric spaces. The results presented in this paper extend and generalize several results from the existing literature. [ABSTRACT FROM AUTHOR]

A vector-b-metric space is a more general space than a b-metric space because it is Riesz space valued. The study of ordered vector spaces is important in economic analysis. In this paper, we prove some common fixed point results for three and four mappings on vector-b-metric space with a graph. Our results extend many known results for three and four mappings on vector metric spaces. [ABSTRACT FROM AUTHOR]

In this paper, we extend and improve a common fixed point theorem of G. Jungck. We utilize the notions of weakly commuting and compatible mappings in probabilistic Banach spaces to prove some common fixed point theorems for improved type Jungck contractions. In addition, we present some examples which support our theorems. [ABSTRACT FROM AUTHOR]

Super Metric Spaces are a ground-breaking generalization of metric spaces that were recently developed by Karapinar and Khojasteh (Filomat, in press). In this paper, we initiate the study of expansive fixed points in the context of the supermetric spaces. Our results may open the door to more expansive fixed point results in a different direction. [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]

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 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 present some generalized multi-valued contraction results on cone metric spaces. We use some maximum and sum types of contractions for a pair of multi-valued mappings to prove some common fixed point theorems on cone metric spaces without the condition of normality. We present an illustrative example for multi-valued contraction mappings to support our work. Moreover, we present a supportive application of nonlinear integral equations to validate our work. This new theory, can be modified in different directions for multi-valued mappings to prove fixed point, common fixed point and coincidence point results in the context of different types of metric spaces with the application of different types of integral equations. [ABSTRACT FROM AUTHOR]

In this paper, we present some generalized multi-valued contraction results on cone metric spaces. We use some maximum and sum types of contractions for a pair of multi-valued mappings to prove some common fixed point theorems on cone metric spaces without the condition of normality. We present an illustrative example for multi-valued contraction mappings to support our work. Moreover, we present a supportive application of nonlinear integral equations to validate our work. This new theory, can be modified in different directions for multi-valued mappings to prove fixed point, common fixed point and coincidence point results in the context of different types of metric spaces with the application of different types of integral equations. [ABSTRACT FROM AUTHOR]

In this paper, we show a counterexample to the new iterative scheme introduced by Rezapour et al. in "A new modified iterative scheme for finding common fixed points in Banach spaces: application in variational inequality problems" [2]. We propose a modified iteration to conclude the convergence result. Moreover, some of our results are established under a weaker assumption. [ABSTRACT FROM AUTHOR]

In this paper, we take advantage of implicit relationships to come up with a new concept called "Aϑ-α-contraction mapping". We utilized our new notion to formulate and prove some common fixed point theorems for two and four self-mappings over complete extended quasi b-metric spaces under a set of conditions. Our main results widen and improve many existing results in the literature. To support our research, we present some examples as applications to our main findings. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to establish common fixed points of six mappings in the context of bicomplex valued metric spaces. In this way, we generalize some previous well-known results from the literature. Moreover, we provide a non-trivial example to demonstrate the authenticity of established outcomes. As an application, we investigate the solution of an Urysohn integral equation by applying our results. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study the existence of a common fixed point for a pair of mappings without assumption of the contractive coeficient being fixed and less than 1. By replacing the fixed contractive coeficient with a nonlinear contractive function, we establish a unique common fixed point theorem for a pair of asymptotically regular self-mappings with either orbital continuity or q-continuity in a metric space. Moreover, by the asymptotical regularity of two approximate mappings, we prove that a pair of nonexpansive and continuous self-mappings, which are defined on a nonempty closed convex subset of a Banach space, have a common fixed point. Some examples are given to illustrate that our results are extensions of a recent result in the existing literature. [ABSTRACT FROM AUTHOR]

In this paper, we prove some common fixed point results for two pairs of weakly compatible mappings satisfying (E:A) property and CLR-property in the framework of S-metric spaces and provide some examples to support the outcomes. We also prove well-posedness of a fixed point problem. Our findings generalize and extend a number of previously published findings. [ABSTRACT FROM AUTHOR]

In this paper, we discuss a new definition of w A -compatible maps in a modular metric space, prove a common fixed point theorem and utilize them to get a solution of a Volterra type integral equation. [ABSTRACT FROM AUTHOR]

In this paper, we prove some common fixed point theorems for mappings satisfying contractive conditions involving rational terms and using control functions in the setting of complex valued S-metric spaces. The esthablished results extend and generalize several results from the existing literature. [ABSTRACT FROM AUTHOR]

The aim of this paper is to inaugurate power graphic (F , ψ) -contraction pair and to establish fixed point results for such mappings defined on tripled partial b-metric spaces endowed with a graph. Then, with some examples, we will show the applications of the our results. [ABSTRACT FROM AUTHOR]