Iterative Scheme for Split Variational Inclusion and a Fixed-Point Problem of a Finite Collection of Nonexpansive Mappings

Abstract

This article is aimed at introducing an iterative scheme to approximate the common solution of split variational inclusion and a fixed-point problem of a finite collection of nonexpansive mappings. It is proven that under some suitable assumptions, the sequences achieved by the proposed iterative scheme converge strongly to a common element of the solution sets of these problems. Some consequences of the main theorem are also given. Finally, the convergence analysis of the sequences achieved from the iterative scheme is illustrated with the help of a numerical example.

Yosida Approximation Iterative Methods for Split Monotone Variational Inclusion Problems

“…It is well known that set-valued monotone operator can be regularized into a single-valued monotone operator by the process known as the Yosida approximation. Yosida approximation is a tool to solve a variational inclusion problem using nonexpansive resolvent operator and has been used to solve various variational inclusions and system of variational inclusions in linear and nonlinear spaces (see, for example, [18,[25][26][27][28][29][30]). Due to the fact that the zero of Yosida approximation operator associated with monotone operator G is the zero of inclusion problem 0 ∈ GðxÞ and inspired by the work of Moudafi, Byrne, Kazmi, and Dilshad et al, our motive is to propose two iterative methods to solve S p MVIP.…”

On a system of monotone variational inclusion problems with fixed-point constraint

“…Moudafi [33], showed that the SVIP (1.7) and (1.8) includes the SFP (1.3) as a special case. Several authors have studied and proposed different iterative methods for solving SVIP (1.7) and (1.8), see for instance [22,27], and the references therein. However, results on SMVIP (1.4) and (1.5) are relatively scanty in the literature.…”

A Unified Inertial Iterative Approach for General Quasi Variational Inequality with Application

“…where α n ∈ [0, 1] and T : K → K is a nonexpansive mapping on a closed convex subset K of a given Banach space. For some recently developed iterative methods, we refer [20][21][22][23][24][25][26][27].…”