A New Hybrid Algorithm for a System of Mixed Equilibrium Problems, Fixed Point Problems for Nonexpansive Semigroup, and Variational Inclusion Problem

Abstract

The purpose of this paper is to consider a shrinking projection method for finding the common element of the set of common fixed points for nonexpansive semigroups, the set of common fixed points for an infinite family of a ξ-strict pseudocontraction, the set of solutions of a system of mixed equilibrium problems, and the set of solutions of the variational inclusion problem. Strong convergence of the sequences generated by the proposed iterative scheme is obtained. The results presented in this paper extend and improve some well-known results in the literature.

Iterative Algorithms for Mixed Equilibrium Problems, System of Quasi-Variational Inclusion, and Fixed Point Problem in Hilbert Spaces

“…Then, we prove strong convergence theorems which are connected with [5,[26][27][28][29]. Our results extend and improve the corresponding results of Jitpeera and Kumam [25], Liou [23], Plubtieng and Punpaeng [20], Petrot et al [24], Peng and Yao [21], Qin et al [22], and some authors.…”

“…In 2011, Jitpeera and Kumam [25] introduced a shrinking projection method for finding the common element of the common fixed points of nonexpansive semigroups, the set of common fixed point for an infinite family, the set of solutions of a system of mixed equilibrium problems, and the set of solution of the variational inclusion problem. Let { }, { }, {V }, { }, and { } be sequences generated by 0 ∈ , 1 = ,…”

An iterative algorithm for finding the solution of a general equilibrium problem system

“…Jitpeera and Kumam [11] considered a shrinking projection method for finding the common element of the set of common fixed points for nonexpansive semigroups, the set of common fixed points for an infinite family of a ξ-strict pseudocontraction, the set of solutions of a system of mixed equilibrium problems, and the set of solutions of the variational inclusion problem. They proved strong convergence theorems of the iterative sequence generated by the shrinking projection method under some suitable conditions in a real Hilbert space.…”

A modified forward‐backward splitting methods for the sum of two monotone operators with applications to breast cancer prediction

“…In recent years, the MVIP (1.1) attracted the increasing attention due to its applicability in many areas such as machine learning, image restoration, signal processing, and like fields. Because of this importance, many iterative algorithms, which are splitting algorithms, have been presented for solving the MVIP(1.1) (see previous works [2][3][4][5][6] ). In this paper, we attempt to find a splitting algorithm that can solve in machine learning when datasets contain some missing attributes value.…”