Multivalued Nonexpansive Mappings Research Articles

Enriched multi-valued nonexpansive mappings in geodesic spaces

Enriched multi-valued nonexpansive mappings in geodesic spaces

Fixed-Point Convergence of Multi-Valued Non-Expansive Mappings with Applications

This paper is dedicated to the advancement of fixed-point results for multi-valued asymptotically non-expansive maps regarding convergence criteria in complete uniformly convex hyperbolic metric spaces that are endowed with a graph. The famous fixed-point theorems of Goebel and Kirk, Khamsi and Khan, along with other recent results in the literature can be obtained as corollaries of these main results. A nice graph and an interesting example are also provided in support of the hypothesis of the main results.

Inertial hybrid gradient method with adaptive step size for variational inequality and fixed point problems of multivalued mappings in Banach spaces

We propose in this article a new inertial hybrid gradient method with self-adaptive step size for approximating a common solution of variational inequality and fixed point problems for an infinite family of relatively nonexpansive multivalued mappings in Banach spaces. Unlike in many existing hybrid gradient methods, here the projection onto the closed convex set is replaced with projection onto some half-space which can easily be implemented. We incorporate into the proposed algorithm inertial term and self-adaptive step size which help to accelerate rate of convergence of iterative schemes. Moreover, we prove a strong convergence theorem without the knowledge of the Lipschitz constant of the monotone operator and we apply our result to find a common solution of constrained convex minimization and fixed point problems in Banach spaces. Finally, we present a numerical example to demonstrate the efficiency of our algorithm in comparison with some recent iterative methods in the literature.

A viscosity-type scheme for optimization problems in Hadamard spaces with applications

In this article, we propose a viscosity-type scheme for approximating a common solution of convex minimization problem, monotone vector field inclusion problem and fixed point problem involving multi-valued nonexpansive mapping in the framework of Hadamard spaces. We obtain a strong convergence theorem for the sequence generated therefrom to a solution of the problem. Furthermore, we apply our results to compute the Fréchet mean, find the mean of probabilities, minimize energy of measurable mappings and solve a problem of two-arm robotic motion control. Finally, we give numerical example to demonstrate the applicability of the method and also issue comparisons with some existing methods. Our results extend and complement some recent results in the literature.

On fixed points of some multivalued mappings under certain function classes

It is well known that the Banach contraction principle implies the existence of fixed points of single-valued mappings. On the other hand, S.B. Nadler has solved the problem that guarantees the existence of fixed point for multivalued mapping. However, we have to emphasize that similar methods are not applied for nonexpansive multivalued mappings. The aim of this study is to investigate the existence of a fixed point on nonexpansive multivalued mappings with the help of function sequences and functions having shifting distance property. In addition, some hypothesis of this work were explained with an interesting example.

A self-adaptive extragradient method for fixed-point and pseudomonotone equilibrium problems in Hadamard spaces

In this work, we study a self-adaptive extragradient algorithm for approximating a common solution of a pseudomonotone equilibrium problem and fixed-point problem for multivalued nonexpansive mapping in Hadamard spaces. Our proposed algorithm is designed in such a way that its step size does not require knowledge of the Lipschitz-like constants of the bifunction. Under some appropriate conditions, we establish the strong convergence of the algorithm without prior knowledge of the Lipschitz constants. Furthermore, we provide a numerical experiment to demonstrate the efficiency of our algorithm. This result extends and complements recent results in the literature.

A New Iterative Sequence of (λ, ρ)-Firmly Nonexpansive Multi-Valued Mappings in Modular Function Spaces with Applications

A New Iterative Sequence of (λ, ρ)-Firmly Nonexpansive Multi-Valued Mappings in Modular Function Spaces with Applications

A new approach to fixed point property of nonexpansive multivalued mappings

A new approach to fixed point property of nonexpansive multivalued mappings

Convergence theorems in Banach spaces for a pair of asymptotically and multi-valued nonexpansive mappings

Convergence theorems in Banach spaces for a pair of asymptotically and multi-valued nonexpansive mappings

Fixed point approximation for a class of generalized nonexpansive multi-valued mappings in Banach spaces

In this paper, we propose a new iteration process, called multi-valued F-iteration process, for the approximation of fixed points. We introduce a new class of multi-valued generalized nonexpansive mappings satisfying a B_{gamma ,mu } property. Moreover, we establish certain weak and strong convergence theorems in uniformly convex Banach spaces. We also discuss the stability of the modified F-iteration process. Furthermore, a numerical example is presented to illustrate the superiority of our results.

Some Results on Invariant Best Approximations in p-Normed Spaces

In this paper we give two theorems in p-normed spaces. The first one is about the existence of fixed point of multivalued nonexpansive mapping and then we use these theorems in the proof of the result( Theorem2.3 )about existence of invariant best approximation. Note that, we need to give Lemma (1.14)

Common Attractive Point Theorems for a Finite Family of Multivalued Nonexpansive Mappings in Banach Spaces

OurmainpurposeofthispaperistointroducethemodifiedMannandIshikawaiteratesforfindingacommonattractivepoint of a finite family of multivalued nonexpansive mappings in the setting of uniformly convex Banach spaces. Weobtain necessary and sufficient conditions to guarantee the strong convergence of the proposed algorithms withoutclosedness of the domain of such mappings. Moreover, we derive some consequences from our main result to fixedpoint result of such mappings. Finally, the numerical results are provided to support our main theorem.

A New Iterative Scheme for Approximating Fixed Points of Suzuki Generalized Multivalued Nonexpansive Mappings

In this paper, we study to approximate fixed points of Suzuki generalized multivalued nonexpansive mappings by using a three-step iterative scheme (1.1) introduced in [17]. We establish some weak and strong convergence results for mappings satisfying condition (C) with the newly proposed iterative scheme in the framework of uniformly convex real Banach spaces.

The New Iterative Approximating of Endpoints of Multivalued Nonexpansive Mappings in Banach Spaces

The purpose of this paper is to introduce the new iteration process to approximate endpoints of multivalued nonexpansive mappings in Banach space. We prove weak and strong convergence theorems of proposed iterative scheme under some suitable assumptions in the framework of a uniformly convex Banach space.

On multi-valued version of M-iteration process

We give a multi-valued version of M iterative process [K. Ullah and M. Arshad, Numerical reckoning fixed points Suzuki’s generalized nonexpansive mappings via new iteration process, Filomat 32 (2018) 187–196] in the setting of Banach spaces. After this, we prove some weak and strong convergence results for the class of multi-valued quasi-nonexpansive mappings (which contains the class of multi-valued nonexpansive mappings) with proper numerical examples using multi-valued version of M-iteration process. These results generalize several well-known comparable results in the literature.

Variational Inequality Problem Involving Multivalued Nonexpansive Mapping in CAT(0) Spaces

Variational Inequality Problem Involving Multivalued Nonexpansive Mapping in CAT(0) Spaces

Inertial hybrid self-adaptive subgradient extragradient method for fixed point of quasi$-\phi-$nonexpansive multivalued mappings and equilibrium problem

In this paper, we propose a new inertial self-adaptive subgradient extragradient algorithm for approximating common solution in the set of pseudomonotone equilibrium problems and the set of fixed point of finite family of quasi$-\phi-$nonexpansive multivalued mappings in real uniformly convex Banach spaces and uniformly smooth Banach spaces. The step size n is chosen self adaptively and estimates of Lipschizt-type constants are dispensed with. Strong convergence of the iterative scheme is established. Our results generalizes and improves several recent results anouced in the literature.

A Modified Proximal Point Algorithm and Some Convergence Results

In this paper, the convergence to minimizers of a convex function of a modified proximal point algorithm involving a single-valued nonexpansive mapping and a multivalued nonexpansive mapping in CAT(0) spaces is studied and a numerical example is given to support our main results.

Measures of noncompactness in modular spaces and fixed point theorems for multivalued nonexpansive mappings

This paper is devoted to state some fixed point results for multivalued mappings in modular vector spaces. For this purpose, we study the uniform noncompact convexity, a geometric property for modular spaces which is similar to nearly uniform convexity in the Banach spaces setting. Using this property, we state several new fixed point theorems for multivalued nonexpansive mappings in modular spaces.

Inertial-Viscosity-Type Algorithms for Solving Generalized Equilibrium and Fixed Point Problems in Hilbert Spaces

In this paper, we introduce a new algorithm of inertial form for solving Split Generalized Equilibrium Problem (SGEP) and Fixed Point Problem (FPP) of multivalued nonexpansive mappings in real Hilbert spaces. Motivated by the viscosity-type method, we incorporate the inertial technique to accelerate the convergence of the proposed method. Here, the viscosity term is a function of the inertial extrapolation sequence and some assumptions on the bifunctions are dispensed with. Under standard and mild assumption of monotonicity and upper hemicontinuity of the SGEP associated mappings, we establish the strong convergence of the scheme which also solves a Variational Inequality Problem (VIP). A numerical example is presented to illustrate the effectiveness and performance of our method as well as comparing it with a related method and conventional inertial-viscosity-type algorithm in the literature.