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The main aim of this paper is to state nonexpansive Maia type fixed point theorems for Ćirić–Prešić operators in normed spaces endowed with a partial order. For this we do a thorough analysis in the hypotheses of our theorems, considering different properties of completeness, compactness, convexity and bounding. We state Maia type fixed point theorems for contraction and nonexpansive Ćirić–Prešić operators, including those defined by a multiply metric function. Fixed point theorems in spaces without a partial order, as well as, corollaries for monotone nonexpansive mappings are stated too. Our theorems generalize and improve results given by Ćirić and Prešić's (Acta Math Univ Comenian (NS) 76:143–147, 2007) and Balazs (Mathematica 10:18–31, 2018) and extend them to nonexpansive operators. [ABSTRACT FROM AUTHOR]

This paper study a class of time-space fractional reaction-diffusion equations with nonlocal initial conditions and construct an abstract theory in fractional power spaces to discuss the results related S-asymptotically ω -periodic mild solutions. When the coefficients are sufficiently small, under the condition that the nonlinear term can grow any number of orders, we discuss the existence and uniqueness of S-asymptotically ω -periodic solutions based on the theory of operator semigroups and fixed point theorem. In addition, we considered the Mittag-Leffler-Ulam-Hyers stability results using the singular type Gronwall inequality and appropriate fractional calculus. The results in the present paper extended the work of (Andrade et al. in Proc Edinb Math Soc 59:65–76, 2016) to the case of time-space fractional nonlocal reaction-diffusion equations. [ABSTRACT FROM AUTHOR]

This paper aims to investigate new coincidence point theorems for self‐maps under an extended rational contraction. Our approach uses the p‐adic distance in partially ordered ultrametric spaces. Furthermore, to illustrate our major discoveries, we give a comprehensive numerical analysis. This study expands on prior research in partially ordered ultrametric spaces to provide a more comprehensive understanding of such spaces using rational contraction. [ABSTRACT FROM AUTHOR]

This study concerns a Krasnoselskii-type fixed point theorem for the sum of two operators A,BA,B in a Banach space EE, where BB is a Reich-type contractive mapping and AA is a k-set contractive mapping. We introduce a class of operators θ:X×X→[1,+∞)\theta :X\times X\to \left[1,+\infty ) satisfying some axioms and use it as a new metric to prove a fixed point theorem in the spirit of Azam et al. [Reich-Krasnoselskii-type fixed point results with applications in integral equations, J. Inequal. Appl. 2023 (2023), 131].

This article aims to provide a modified Noor iterative scheme to approximate the fixed points of generalized nonexpansive mappings with property (EE) called MN-iteration. We establish the strong and weak convergence results in a uniformly convex Banach space. Additionally, numerical experiments of the iterative technique are demonstrated using a signal recovery application in a compressed sensing situation. Ultimately, an illustrative analysis regarding Noor, SP-, and MN-iteration procedures is obtained via polysomnographic techniques. The images obtained are called polynomiographs. Polynomiographs have importance for both the art and science aspects. The obtained graphs describe the pattern of complex polynomials and also the convergence properties of the iterative method. They can also be used to increase the functionality of the existing polynomiography software.

The problem of common solutions for nonlinear equations has significant theoretical and practical value. In this article, we first introduce a new concept of a pair of (α,Θ)\left(\alpha ,\Theta )-type contractions, and then, we present some common fixed point results for the contractions in complete metric spaces. Finally, our results are applied to consider the existence, uniqueness and approximation of common solutions for two classes of nonlinear fractional differential equations.

Krasnoselskii’s iteration is a classical and important method for approximating the fixed point of an operator that satisfies certain conditions. Many authors have used this approach to obtain several famous fixed point theorems for different types of operators. It is well known that Kirk’s iteration can be seen as a generalization of Krasnoselskii’s iteration, in which the iterates are generated by a certain generalized averaged mapping. This approximation method is of great practical significance because the iterative formula contains more information related to the operator in question. The purpose of this study is to define weak (αn,βi)\left({\alpha }_{n},{\beta }_{i})-convex orbital Lipschitz operators. These concepts not only extend the previously introduced Popescu-type convex orbital (λ,β)\left(\lambda ,\beta )-Lipschitz operators in Fixed-point results for convex orbital operators, (Demonstr. Math. 56 (2023), 20220184), but also encompass many classical contractive operators. Popescu also proved a fixed point result for his proposed operator using the graphic contraction principle and obtained an approximation of the fixed point with Krasnoselskii’s iterates. To extend Popescu’s main results from Krasnoselskii’s iterative scheme to Kirk’s iterative scheme, several fixed point theorems are established, in which an appropriate Kirk’s iterative algorithm can be used to approximate the fixed point of a kk-fold averaged mapping associated with our presented convex orbital Lipschitz operators. These results not only generalize, but also complement the existing results documented in the previous literature.

In this study, we introduce the following additive functional equation:g(λu+v+2y)=λg(u)+g(v)+2g(y)g\left(\lambda u+v+2y)=\lambda g\left(u)+g\left(v)+2g(y) for all λ∈C\lambda \in {\mathbb{C}}, all unitary elements u,vu,v in a unital Poisson C*{C}^{* }-algebra PP, and all y∈Py\in P. Using the direct method and the fixed point method, we prove the Hyers-Ulam stability of the aforementioned additive functional equation in unital Poisson C*{C}^{* }-algebras. Furthermore, we apply to study Poisson C*{C}^{* }-algebra homomorphisms and Poisson C*{C}^{* }-algebra derivations in unital Poisson C*{C}^{* }-algebras.

Developing a model of fractional differential systems and studying the existence and stability of a solution is considebly one of the most important topics in the field of analysis. Therefore, this manuscript was dedicated to deriving a new type of fractional system that arises from the combination of three sequential fractional derivatives with fractional pantograph equations. Also, the fixed-point technique was used to evaluate the existence and uniqueness of solutions to the supposed hybrid model. Furthermore, stability results for the intended system in the sense of the Mittag-Leffler-Ulam have been investigated. Ultimately, an illustrative example has been highlighted in order to reinforce the theoretical results and suggest applications for this article.

The objective of this study is to determine the criteria under which the infinite system of integral equations in three variables has a solution in the Banach tempering sequence space c0β{c}_{0}^{\beta } and ℓ1β{\ell }_{1}^{\beta }, utilizing the Meir-Keeler condensing operators. Our research builds upon the findings of Malik and Jalal. Furthermore, we provide illustrative examples to demonstrate the implications of our established conditions.

In this study, we generalize fuzzy metric-like, non-Archimedean fuzzy metric-like, and all the variants of fuzzy metric spaces. We propose the idea of fuzzy metric-unlike and non-Archimedean fuzzy metric-unlike, respectively. We also propose the idea of (α,F)\left(\alpha ,F)-Geraghty-type generalized FF-contraction mappings utilizing fuzzy metric-unlike and non-Archimedean fuzzy metric-unlike spaces. We investigate the presence of unique fixed points using the recently introduced contraction mappings. In order to complement our study, we consider an application to dynamic market equilibrium.

This article presents the notions of extended b-gauge space (U,Qφ;Ω)\left(U,{Q}_{\varphi ;\Omega }) and extended Jφ;Ω{{\mathcal{J}}}_{\varphi ;\Omega }-families of generalized extended pseudo-b-distances on UU. Furthermore, we look at these extended Jφ;Ω{{\mathcal{J}}}_{\varphi ;\Omega }-families on UU and define the extended Jφ;Ω{{\mathcal{J}}}_{\varphi ;\Omega }-sequential completeness. We also look into some fixed and periodic point theorems for set-valued mappings in the new space with a graph that does not meet the completeness condition of the space. Additionally, this article includes some examples to explain the corresponding results and highlights some important consequences of our obtained results.

We study the asymptotic behavior of trajectories of the continuous dynamical system(CDS) associated with the discrete viscosity approximation method for fixed point problem of nonexpansive mapping (DDS) which was introduced by Moudafi (J Math Anal Appl 241:46–55, 2000). We establish that the trajectories x(t) of the continuous dynamical system (CDS) has an asymptotic behavior similar to the behavior of the sequences (x n) generated by the discrete viscosity approximation (DDS) [ABSTRACT FROM AUTHOR]

The note is concerned with the functional equation λ 1 H 1 (f (x)) + λ 2 H 2 (f 2 (x)) + ⋯ + λ n H n (f n (x)) = F (x) , which is a generalised form of the so-called polynomial-like iterative equation. We investigate the existence of nondecreasing convex (both usual and higher order) solutions to this equation on open intervals using the Schauder fixed point theorem. The results supplement those proved by Trif (Aquat Math, 79:315–327, 2010) for the polynomial-like iterative equation by generalising them to a greater extent. This assertion is supported by some examples illustrating their applicability. [ABSTRACT FROM AUTHOR]

This work presents the concept of controlled dislocated metric spaces, and the Banach contraction principle in these spaces is examined. Next, we provide extensive examples of numerical convergence of fixed points to demonstrate the practical implications of such spaces. Along with specific instances, it presents the idea of a rational contraction of the [Formula: see text]type to determine common fixed points in such spaces. Moreover, numerical analysis and graphical comparisons are used to further assess the existence of common fixed points based on the provided notions. Lastly, using these ideas to solve a Volterra integral equation shows how useful they are for finding common solutions, improving our comprehension of fixed point theory in these spaces, and creating new avenues for applications.

In this paper, we introduce a new class of nonlinear mappings and compare it to other classes of nonlinear mappings that have appeared in the literature. We establish various existence and convergence theorems for this class of mappings under different assumptions in Banach spaces, particularly Banach spaces with a normal structure. In addition, we provide examples to substantiate the findings presented in this study. We prove the existence of a common fixed point for a family of commuting α\alpha -partially nonexpansive self-mappings. Furthermore, we extend the results reported by Suzuki (Fixed point theorems and convergence theorems for some generalized nonexpansive mappings, J. Math. Anal. Appl. 340 (2008), no. 2, 1088–1095), Llorens-Fuster (Partially nonexpansive mappings, Adv. Theory Nonlinear Anal. Appl. 6 (2022), no. 4, 565–573), and Dhompongsa et al. (Edelstein’s method and fixed point theorems for some generalized nonexpansive mappings, J. Math. Anal. Appl. 350 (2009), no. 1, 12–17). Finally, we present an open problem concerning the existence of fixed points for α\alpha -partially nonexpansive mappings in the context of uniformly nonsquare Banach spaces.

In this manuscript, we prove new extensions of Nashine, Wardowski, Feng-Liu, and Ćirić-type contractive inequalities using orbitally lower semi-continuous functions in an orbitally complete bb-metric space. We accomplish new multivalued common fixed point results for two families of dominated set-valued mappings in an ordered complete orbitally bb-metric space. Some new definitions and illustrative examples are given to validate our new results. To show the novelty of our results, applications are given to obtain the solution of nonlinear integral and fractional differential equations. Our results expand the hypothetical consequences of Nashine et al. (Feng–Liu-type fixed point result in orbital b-metric spaces and application to fractal integral equation, Nonlinear Anal. Model. Control. 26 (2021), no. 3, 522–533) and Rasham et al. (Common fixed point results for new Ciric-type rational multivalued-contraction with an application, J. Fixed Point Theory Appl. 20 (2018), no. 1, Paper No. 45).

This manuscript is devoted to constructing a novel iterative scheme and reckoning of fixed points for generalized contraction mappings in hyperbolic spaces. Also, we establish Δ\Delta and strong convergence results by the considered iteration under the class of mappings satisfying condition (E). Moreover, some qualitative results of the suggested iteration, like weak w2{w}^{2}-stability and data dependence results, are discussed. Furthermore, to test the efficiency and effectiveness of the proposed iteration, practical experiments are given. To support the theoretical results, illustrative examples are presented. Finally, our results improve and generalize several classical results in the literature of fixed point iterations.

In this article, we first study the inverse source problem for parabolic with memory term. We show that our problem is ill-posed in the sense of Hadamard. Then, we construct the convergence result when the parameter tends to zero. We also investigate the regularized solution using the Fourier truncation method. The error estimate between the regularized solution and the exact solution is obtained.

In this study, we solve the system of additive functional equations: h(x+y)=h(x)+h(y),g(x+y)=f(x)+f(y),2fx+y2=g(x)+g(y),\left\{\begin{array}{l}h\left(x+y)=h\left(x)+h(y),\\ g\left(x+y)=f\left(x)+f(y),\\ 2f\left(\frac{x+y}{2}\right)=g\left(x)+g(y),\end{array}\right. and we investigate the stability of (homomorphism, derivation)-systems in Banach algebras.

The present article deals with new fixed point theorems by means of GG-strongly contractive maps. The research findings are demonstrated in a spherically complete ultrametric space with a graph for single-valued mappings. The special cases of the results that extend the current ones are offered, along with some examples that illustrate our results. Besides, an application utilized in dynamic programming that endorses the acquired observations is also provided.

Abstract In this work, we obtain fixed point theorems and convergence theorems for Suzuki-generalized nonexpansive mappings in complete $$CAT_p(0)$$ C A T p ( 0 ) metric spaces for $$p\ge 2$$ p ≥ 2 . Our results extend and improve many results in the literature.

Jleli and Samet in [On a new generalization of metric spaces, J. Fixed Point Theory Appl. 20 (2018), 128 (20 pages)] introduced the notion of ℱ -metric space as a generalization of traditional metric space and proved Banach contraction principle in the setting of this generalized metric space. The objective of this article is to use ℱ -metric space and establish some common fixed point theorems for (β\beta -ψ\psi )-contractions. Our results expand, generalize, and consolidate several known results in the literature. As applications of the main result, the solution for fuzzy initial-value problems in the background of a generalized Hukuhara derivative was discussed.

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.

We introduce the concept of generalized suprametric spaces, which subsumes some existing abstract metric spaces. Then, we show the existence of fixed points for maps satisfying nonlinear contractions involving either extended comparison or ρ\rho -subhomogeneous functions. This study was carried out in generalized suprametric spaces as well as partially ordered generalized suprametric spaces. Some related results in JS-metric spaces and in bb-suprametric spaces are improved or extended.

The aim is to utilize a new metric called an MvbM_{\rm{v}}^{\rm{b}}–metric which is an improvement and generalization of Mv−metric to revisit the celebrated Banach and Sehgal contractions in MvbM_{\rm{v}}^{\rm{b}}–metric space. We demonstrate that the collection of open balls forms a basis on MvbM_{\rm{v}}^{\rm{b}}-metric space. Further, we give some examples for the verification of established results. Towards the end, we solve a non-linear matrix equation and an equation of rotation of a hanging cable to substantiate the utility of these extensions.

The aim is to introduce some relation theoretic variants of F−contraction in an F−metric space endowed with a binary relation R and to prove results for its fixed point. In the sequel, several classes of contractions are sharpened, generalized, and improved. Numerical examples are presented to illustrate the theoretical conclusions. As applications of the main results, we solve a Dirichlet-Neumann initial value problem and two Dirichlet boundary value problems.

We are interested in the existence of mild solutions for a class of partial integrodifferential inclusions in infinite dimensional Banach spaces. First, we show the existence of mild solutions with the help of a scale of Banach spaces, the theory of resolvent operators, and the fixed point theory for the measure of non-compactness. Moreover, we examine the existence of asymptotically almost periodic solutions for our problem. Finally, an example of the abstract results is provided.

By combining monotonicity theory related to the parametric version of the Browder-Minty theorem with fixed point arguments, hybrid existence results for a system of two operator equations are obtained. Applications are given to a system of boundary value problems with mixed nonlocal and Dirichlet conditions.

In this article, we prove ergodic convergence for a sequence of nonexpansive mappings in Hadamard (complete CAT(0){\rm{CAT}}\left(0)) spaces. Our result extends the nonlinear ergodic theorem by Baillon for nonexpansive mappings from Hilbert spaces to Hadamard spaces. We further establish the standard nonlinear ergodic theorem and apply our results to the problem of finding a common fixed point of a countable family of nonexpansive mappings. Finally, we propose some applications of our results to solve convex optimization problems in Hadamard spaces.

This paper explores the concept of normal structure by introducing a generalized form known as P-proximal normal structure. Focusing on the framework of Hausdorff locally convex spaces, the study establishes optimal proximity outcomes for both cyclic and noncyclic relatively P-nonexpansive mappings. Furthermore, the paper presents in the realm of probabilistic normed spaces, considered as instances of Hausdorff locally convex spaces, some theorems that address the existence of best proximity points within this context.

In this paper, we prove the following generalization of the classical Darbo fixed point principle : Let X be a Banach space and µ be a montone measure of noncompactness on X which satisfies the generalized Cantor intersection property. Let C be a nonempty bounded closed convex subset of X and T : C → C be a continuous mapping such that for any countable set Ω ⊂ C, we have µ(T(Ω)) ≤ kµ(Ω), where k is a constant, 0 ≤ k < 1. Then T has at least one fixed point in C. The proof is based on a combined use of topological methods and partial ordering techniques and relies on the Schauder and the Knaster-Tarski fixed point principles.

This article analyzes the JK iteration process with the class of mappings that are essentially endowed with a condition called condition (E). The convergence of the iteration toward a fixed point of a specific mapping satisfying the condition (E) is obtained under some possible mild assumptions. It is worth mentioning that the iteration process JK converges better toward a fixed point compared to some prominent iteration processes in the literature. This fact is confirmed by a numerical example. Furthermore, it has been shown that the iterative scheme JK is stable in the setting of generalized contraction. The data dependence result is also established. Our results are new in the iteration theory and extend some recently announced results of the literature.

In this work, we investigate the existence of mild solutions in the α\alpha -norm for a class of nonlocal integrodifferential equations. We employ the theory of resolvent operators introduced by R. Grimmer. The Leray-Schauder alternative is the principal working tool for our analysis.

We improve the rational contractive condition and prove the common fixed point in the dislocated metric spaces. In addition, the new generalized rational contraction has existence of a common solution for a system of integral equations.

Recently, Abbas et al. [Enriched multivalued contractions with applications to differential inclusions and dynamic programming, Symmetry 13(8) (2021), 1350] obtained an interesting generalization of the Nadler fixed point theorem by introducing the concept of enriched multivalued contraction in the framework of Banach spaces. In this article, we define a new class of metrics on the family of closed and bounded subsets of a given metric space. Furthermore, fixed point theorems were established for enriched multi-valued contractions by substituting the Hausdorff metric with metrics from a specific class that are either metrically or sequentially equivalent to the Hausdorff metric. Some examples are provided to illustrate the concepts and results presented herein. These results improve, unify, and generalize several comparable results in the literature.

Very recently, P. Saha et al. [A global optimality result in probabilistic spaces using control function. Optimization. 2021;70:2387–2400] studied the existence of best proximity points for Banach type ϕ-proximal contractions in the framework of Menger probabilistic metric spaces. In this paper, we present a simple proof of their main existence result which is based on a fixed point theorem for ϕ-contractive self-mappings in complete Menger PM-spaces due to B.S. Choudhury and K. Das [A new contraction principle in Menger spaces. Acta Math Sin. 2008;24:13791386]. [ABSTRACT FROM AUTHOR]

In this article, weak and strong convergence theorems of the M-iteration method for 𝒢-nonexpansive mapping in a uniformly convex Banach space with a directed graph were established. Moreover, weak convergence theorem without making use of Opial’s condition is proved. The rate of convergence between the M-iteration and some other iteration processes in the literature was also compared. Specifically, our main result shows that the M-iteration converges faster than the Noor and SP iterations. Finally, the numerical examples to compare convergence behavior of the M-iteration with the three-step Noor iteration and the SP-iteration were given. As application, some numerical experiments in real-world problems were provided, focused on image deblurring and signal recovering problems.

Abstract This research deals with Krasnoselskii’s fixed point theorem where the entries operators do not need to be G-weakly compact and contraction. These results were obtained by using the so-called generalized measure of weak noncompactness and some user-friendly lemmas. Moreover, these gained fixed point results are applied to study the existence of solutions of a coupled system for integral equations in the generalized Banach space C ( [ 0 , 1 ] , E 1 ) × C ( [ 0 , 1 ] , E 2 ) $\mathcal{{ C }} ( [0,1], E_{1} )\times \mathcal{{ C }} ( [0,1], E_{2} ) $ .

The paradigm of choice practice represents the psychological theory of learning in the development of moral judgment. It is concerned with evaluating the implications of several choices and selecting one of them to implement. The goal of this work is to provide a generic functional equation to observe the behavior of animals in such circumstances. Our suggested functional equation can be employed to describe several well-known psychology and learning theories. The fixed point theorem proposed by Banach is utilized to show that the solution of a given functional problem exists and is unique. In addition, the stability of the given functional equation’s solution is discussed in terms of the Hyers-Ulam and Hyers-Ulam-Rassias results. Furthermore, two examples are provided to highlight the relevance of the significant outcomes in the context of the literature.

The primary goal of this research is to investigate the approximate numerical solution of variational inequalities using quasimonotone operators in infinite-dimensional real Hilbert spaces. In this study, the sequence obtained by the proposed iterative technique for solving quasimonotone variational inequalities converges strongly toward a solution due to the viscosity-type iterative scheme. Furthermore, a new technique is proposed that uses an inertial mechanism to obtain strong convergence iteratively without the requirement for a hybrid version. The fundamental benefit of the suggested iterative strategy is that it substitutes a monotone and non-monotone step size rule based on mapping (operator) information for its Lipschitz constant or another line search method. This article also provides a numerical example to demonstrate how each method works.

Abstract We establish a relationship between asymptotic regularity and common stationary points of multivalued mappings on a metric space. As a consequence of our results, we obtain a new common fixed point result for two asymptotically regular single-valued mappings. Our work significantly improves and complements comparable results in the literature.

Abstract In this paper, we study a nonlinear fractional p-Laplacian boundary value problem containing both left Riemann–Liouville and right Caputo fractional derivatives with initial and integral conditions. Some new results on the existence and uniqueness of a solution for the model are obtained as well as the Ulam stability of the solutions. Two examples are provided to show the applicability of our results.

This paper deals with the existence and uniqueness of common fixed points in metric and dislocated metric spaces. In addition, an application and some illustrative examples are given in order to justify the validity and credibility of our results, also, their superiority over some similar theorems existing in unique common fixed points theory’s domain.

The present article is devoted to the positive periodic solution for impulsive discrete hematopoiesis model. This model is described by a first-order nonlinear difference equation with multiple delays and impulses. The existence result is obtained by applying the Krasnosel’skii fixed point theorem. A sufficient condition that guarantees that there is at least one positive periodic solution is established. Moreover, illustrative example and numerical simulation analysis are provided to show the existence of positive periodic solutions and the effect of impulses on positive periodic solutions.

The notion of approximate fixed point sequence, emphasized in Chidume (Geometric properties of Banach spaces and nonlinear iterations. Lecture Notes in Mathematics, 1965. Springer-Verlag London, Ltd., London, 2009), is a very useful tool in proving convergence theorems for fixed point iterative schemes in the class of nonexpansive-type mappings. In the present paper, our aim is to present simple and unified alternative proofs of some classical fixed point theorems emerging from Banach contraction principle, by using a technique based on the concepts of approximate fixed point sequence and graphic contraction. [ABSTRACT FROM AUTHOR]

In this article, without requiring solidness of the underlying cone, a kind of new convergence for sequences in cone bb-metric spaces over Banach algebras and a new kind of completeness for such spaces, namely, wrtn-completeness, are introduced. Under the condition that the cone bb-metric spaces are wrtn-complete and the underlying cones are normal, we establish a common fixed point theorem of contractive conditions with vector-valued coefficients in the non-solid cone bb-metric spaces over Banach algebras, where the coefficients s≥1s\ge 1. As consequences, we obtain a number of fixed point theorems of contractions with vector-valued coefficients, especially the versions of Banach contraction principle, Kannan’s and Chatterjea’s fixed point theorems in non-solid cone bb-metric spaces over Banach algebras. Moreover, some valid examples are presented to support our main results.

The aim of this article is to introduce α\alpha -ψ\psi -proximal contraction in the setting of ℱ-metric space and prove the existence of best proximity points for these contractions. As applications of our main results, we obtain coupled best proximity points on ℱ-metric space equipped with an arbitrary binary relation.

In this article, we propose a Halpern-type subgradient extragradient algorithm for solving a common element of the set of solutions of variational inequality problems for continuous monotone mappings and the set of f-fixed points of continuous f-pseudocontractive mappings in reflexive real Banach spaces. In addition, we prove a strong convergence theorem for the sequence generated by the algorithm. As a consequence, we obtain a scheme that converges strongly to a common f-fixed point of continuous f-pseudocontractive mappings and a scheme that converges strongly to a common zero of continuous monotone mappings in Banach spaces. Furthermore, we provide a numerical example to illustrate the implementability of our algorithm.

In this paper we formulate a setvalued fixed point problem by combining four prevalent trends of fixed point theory. We solve the problem by showing that the set of fixed points is nonempty. Further we have a data dependence result pertaining to the problem and also a stability result for the fixed point sets. The main result is extended to metric spaces with a graph. The results are obtained without the use of metric completeness assumption which is replaced by some other conditions suitable for solving the fixed point problem. There are some consequences of the main result. The main result is illustrated with an example.