Strong convergence of an iterative method for solving the multiple-set split equality fixed point problem in a real Hilbert space

2016 ◽  
Vol 111 (4) ◽  
pp. 983-998 ◽  
Author(s):  
Dinh Minh Giang ◽  
Jean Jacques Strodiot ◽  
Van Hien Nguyen
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Iterative Method ◽  
Strong Convergence ◽  
Real Hilbert Space ◽  
Fixed Point Problem ◽  
Point Problem

scholarly journals Hybrid Algorithms for Variational Inequalities Involving a Strict Pseudocontraction

Symmetry ◽  
2019 ◽  
Vol 11 (12) ◽  
pp. 1502
Author(s):  
Sun Young Cho
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Variational Inequality ◽  
Variational Inequalities ◽  
Variational Inequality Problem ◽  
Real Hilbert Space ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Strict Pseudocontraction ◽  
Adaptive Step

In a real Hilbert space, we investigate the Tseng’s extragradient algorithms with hybrid adaptive step-sizes for treating a Lipschitzian pseudomonotone variational inequality problem and a strict pseudocontraction fixed-point problem, which are symmetry. By imposing some appropriate weak assumptions on parameters, we obtain a norm solution of the problems, which solves a certain hierarchical variational inequality.

scholarly journals Explicit Scheme for Fixed Point Problem for Nonexpansive Semigroup and Split Equilibrium Problem in Hilbert Space

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Pei Zhou ◽  
Gou-Jie Zhao
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Iterative Method ◽  
Equilibrium Problems ◽  
Fixed Point Problem ◽  
Explicit Scheme ◽  
Common Element ◽  
Nonexpansive Semigroup ◽  
Point Problem ◽  
Split Equilibrium Problem

We establish an iterative method for finding a common element of the set of fixed points of nonexpansive semigroup and the set of split equilibrium problems. Under suitable conditions, some strong convergence theorems are proved. Our works improve previous results for nonexpansive semigroup.

scholarly journals Cyclic Iterative Method for Strictly Pseudononspreading in Hilbert Space

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Bin-Chao Deng ◽  
Tong Chen ◽  
Zhi-Fang Li
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Variational Inequality ◽  
Iterative Method ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Convex Subset ◽  
Real Hilbert Space ◽  
Cyclic Algorithm ◽  
The Common

Let{Ti}i=1NbeNstrictly pseudononspreading mappings defined on closed convex subsetCof a real Hilbert spaceH. Consider the problem of finding a common fixed point of these mappings and introduce cyclic algorithms based on general viscosity iteration method for solving this problem. We will prove the strong convergence of these cyclic algorithm. Moreover, the common fixed point is the solution of the variational inequality〈(γf-μB)x*,v-x*〉≤0,∀v∈⋂i=1NFix(Ti).

scholarly journals Strong convergence for monotone bilevel equilibria with constraints of variational inequalities and fixed points using subgradient extragradient implicit rule

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Long He ◽  
Yun-Ling Cui ◽  
Lu-Chuan Ceng ◽  
Tu-Yan Zhao ◽  
Dan-Qiong Wang ◽  
...  
Keyword(s):  
Fixed Point ◽  
Variational Inequalities ◽  
Strong Convergence ◽  
Equilibrium Problem ◽  
Real Hilbert Space ◽  
Nonexpansive Mappings ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Common Solution ◽  
Implicit Rule

AbstractIn a real Hilbert space, let GSVI and CFPP represent a general system of variational inequalities and a common fixed point problem of a countable family of nonexpansive mappings and an asymptotically nonexpansive mapping, respectively. In this paper, via a new subgradient extragradient implicit rule, we introduce and analyze two iterative algorithms for solving the monotone bilevel equilibrium problem (MBEP) with the GSVI and CFPP constraints, i.e., a strongly monotone equilibrium problem over the common solution set of another monotone equilibrium problem, the GSVI and the CFPP. Some strong convergence results for the proposed algorithms are established under the mild assumptions, and they are also applied for finding a common solution of the GSVI, VIP, and FPP, where the VIP and FPP stand for a variational inequality problem and a fixed point problem, respectively.

scholarly journals Strong Convergence for the Split Common Fixed-Point Problem for Total Quasi-Asymptotically Nonexpansive Mappings in Hilbert Space

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Lawan Bulama Mohammed ◽  
A. Kılıçman
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Nonexpansive Mappings ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Common Fixed Point Problem ◽  
Asymptotically Nonexpansive ◽  
Split Common Fixed Point

In this paper, we study and modify the algorithm of Kraikaew and Saejung for the class of total quasi-asymptotically nonexpansive case so that the strong convergence is guaranteed for the solution of split common fixed-point problems in Hilbert space. Moreover, we justify our result through an example. The results presented in this paper not only extend the result of Kraikaew and Saejung but also extend, improve, and generalize some existing results in the literature.

scholarly journals Strong Convergence Algorithm for Split Equilibrium Problems and Hierarchical Fixed Point Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Abdellah Bnouhachem
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Real Hilbert Space ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Split Equilibrium Problem ◽  
Special Cases ◽  
Hierarchical Fixed Point ◽  
The Common ◽  
Hierarchical Fixed Point Problems

The purpose of this paper is to investigate the problem of finding the approximate element of the common set of solutions of a split equilibrium problem and a hierarchical fixed point problem in a real Hilbert space. We establish the strong convergence of the proposed method under some mild conditions. Several special cases are also discussed. Our main result extends and improves some well-known results in the literature.

scholarly journals Common Solution for a Finite Family of Equilibrium Problems, Quasi-Variational Inclusion Problems and Fixed Points on Hadamard Manifolds

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1161
Author(s):  
Jinhua Zhu ◽  
Jinfang Tang ◽  
Shih-sen Chang ◽  
Min Liu ◽  
Liangcai Zhao
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Equilibrium Problems ◽  
Fixed Point Problem ◽  
Finite Family ◽  
Variational Inclusion ◽  
Point Problem ◽  
Hadamard Manifolds ◽  
Inclusion Problems ◽  
Common Solution

In this paper, we introduce an iterative algorithm for finding a common solution of a finite family of the equilibrium problems, quasi-variational inclusion problems and fixed point problem on Hadamard manifolds. Under suitable conditions, some strong convergence theorems are proved. Our results extend some recent results in literature.

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