scholarly journals Strong and Weak Convergence Theorems for Equilibrium Problems and Weak Relatively Uniformly Nonexpansive Multivalued Mappings in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
Zi-Ming Wang
Keyword(s):  
Weak Convergence ◽  
Equilibrium Problem ◽  
Equilibrium Problems ◽  
Fixed Point Problem ◽  
Common Element ◽  
Multivalued Mappings ◽  
Point Problem ◽  
Strong And Weak Convergence ◽  
Convergence Results ◽  
The Common

Equilibrium problem and fixed point problem are considered. A general iterative algorithm is introduced for finding a common element of the set of solutions to the equilibrium problem and the common set of fixed points of two weak relatively uniformly nonexpansive multivalued mappings. Furthermore, strong and weak convergence results for the common element in the two sets mentioned above are established in some Banach space.

scholarly journals Some Results for Split Equality Equilibrium Problems in Banach Spaces

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 194
Author(s):  
Zhaoli Ma ◽  
Lin Wang ◽  
Yeol Cho
Keyword(s):  
Fixed Point ◽  
Weak Convergence ◽  
Banach Spaces ◽  
Equilibrium Problems ◽  
Nonexpansive Mappings ◽  
Fixed Point Problem ◽  
Common Element ◽  
Point Problem ◽  
Convex Minimization Problem ◽  
Strong And Weak Convergence

In this paper, a new algorithm for finding a common element of a split equality fixed point problem for nonexpansive mappings and split equality equilibrium problem in three Banach spaces is introduced. Also, some strong and weak convergence theorems for the proposed algorithm are proved. Finally, the main results obtained in this paper are applied to solve the split equality convex minimization problem.

scholarly journals Strong Convergence Results of Split Equilibrium Problems and Fixed Point Problems

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Li-Jun Zhu ◽  
Hsun-Chih Kuo ◽  
Ching-Feng Wen
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Equilibrium Problem ◽  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Iterative Scheme ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Split Equilibrium Problem ◽  
Convergence Results

In this paper, we investigate the split equilibrium problem and fixed point problem in Hilbert spaces. We propose an iterative scheme for solving such problem in which the involved equilibrium bifunctions f and g are pseudomonotone and monotone, respectively, and the operators S and T are all pseudocontractive. We show that the suggested scheme converges strongly to a solution of the considered problem.

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 A novel algorithm for approximating common solution of a system of monotone inclusion problems and common fixed point problem

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Mohammad Eslamian ◽  
Ahmad Kamandi
Keyword(s):  
Fixed Point Problem ◽  
Common Fixed Points ◽  
Common Element ◽  
Feasibility Problem ◽  
Point Problem ◽  
Monotone Inclusion ◽  
Splitting Algorithm ◽  
Inclusion Problems ◽  
Inertial Algorithm ◽  
The Common

<p style='text-indent:20px;'>In this paper, we study the problem of finding a common element of the set of solutions of a system of monotone inclusion problems and the set of common fixed points of a finite family of generalized demimetric mappings in Hilbert spaces. We propose a new and efficient algorithm for solving this problem. Our method relies on the inertial algorithm, Tseng's splitting algorithm and the viscosity algorithm. Strong convergence analysis of the proposed method is established under standard and mild conditions. As applications we use our algorithm for finding the common solutions to variational inequality problems, the constrained multiple-set split convex feasibility problem, the convex minimization problem and the common minimizer problem. Finally, we give some numerical results to show that our proposed algorithm is efficient and implementable from the numerical point of view.</p>

scholarly journals Convergence Theorems for Common Solutions of Split Variational Inclusion and Systems of Equilibrium Problems

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 255
Author(s):  
Yan Tang ◽  
Yeol Cho
Keyword(s):  
Equilibrium Problems ◽  
Fixed Point Problem ◽  
Variational Inclusion ◽  
Common Element ◽  
Inclusion Problem ◽  
Point Problem ◽  
Step Size ◽  
Convergence Theorems ◽  
Common Solution ◽  
Variational Inclusion Problem

In this paper, the split variational inclusion problem (SVIP) and the system of equilibrium problems (EP) are considered in Hilbert spaces. Inspired by the works of Byrne et al., López et al., Moudafi and Thukur, Sobumt and Plubtieng, Sitthithakerngkiet et al. and Eslamian and Fakhri, a new self-adaptive step size algorithm is proposed to find a common element of the solution set of the problems SVIP and EP. Convergence theorems are established under suitable conditions for the algorithm and application to the common solution of the fixed point problem, and the split convex optimization problem is considered. Finally, the performances and computational experiments are presented and a comparison with the related algorithms is provided to illustrate the efficiency and applicability of our new algorithms.

scholarly journals Strong Convergence Theorems for Mixed Equilibrium Problem and AsymptoticallyI-Nonexpansive Mapping in Banach Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Bin-Chao Deng ◽  
Tong Chen ◽  
Yi-Lin Yin
Keyword(s):  
Strong Convergence ◽  
Equilibrium Problem ◽  
Hybrid Algorithm ◽  
Nonexpansive Mappings ◽  
Fixed Point Problem ◽  
Common Element ◽  
Point Problem ◽  
Mixed Equilibrium Problem ◽  
Convergence Theorems ◽  
Mixed Equilibrium

This paper aims to use a hybrid algorithm for finding a common element of a fixed point problem for a finite family of asymptotically nonexpansive mappings and the set solutions of mixed equilibrium problem in uniformly smooth and uniformly convex Banach space. Then, we prove some strong convergence theorems of the proposed hybrid algorithm to a common element of the above two sets under some suitable conditions.

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

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
M. Dilshad ◽  
A. F. Aljohani ◽  
M. Akram
Keyword(s):  
Fixed Point ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Fixed Point Problem ◽  
Variational Inclusion ◽  
Common Element ◽  
Finite Collection ◽  
Point Problem ◽  
Common Solution ◽  
The Common

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.

scholarly journals Modified Krasnoselski–Mann iterative method for hierarchical fixed point problem and split mixed equilibrium problem

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Jong Kyu Kim ◽  
Prashanta Majee
Keyword(s):  
Fixed Point ◽  
Iterative Method ◽  
Equilibrium Problem ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Mixed Equilibrium Problem ◽  
Convergence Results ◽  
Hierarchical Fixed Point ◽  
Mixed Equilibrium ◽  
Split Mixed Equilibrium Problem

Abstract In this paper, we introduce a modified Krasnoselski–Mann type iterative method for capturing a common solution of a split mixed equilibrium problem and a hierarchical fixed point problem of a finite collection of k-strictly pseudocontractive nonself-mappings. Many of the algorithms for solving the split mixed equilibrium problem involve a step size which depends on the norm of a bounded linear operator. Since the computation of the operator norm is very difficult, we formulate our iterative algorithm in such a way that the implementation of the proposed algorithm does not require any prior knowledge of operator norm. Weak convergence results are established under mild conditions. We also establish strong convergence results for a certain class of hierarchical fixed point and split equilibrium problem. Our results generalize some important results in the recent literature.

scholarly journals Strong Convergence Results for Equilibrium Problems and Fixed Point Problems for Multivalued Mappings

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
J. Vahidi ◽  
A. Latif ◽  
M. Eslamian
Keyword(s):  
Hilbert Space ◽  
Strong Convergence ◽  
Equilibrium Problems ◽  
Common Fixed Points ◽  
Finite Family ◽  
Common Element ◽  
Multivalued Mappings ◽  
Viscosity Approximation Method ◽  
Viscosity Approximation ◽  
Convergence Results

Using viscosity approximation method, we study strong convergence to a common element of the set of solutions of an equilibrium problem and the set of common fixed points of a finite family of multivalued mappings satisfying the condition (E) in the setting of Hilbert space. Our results improve and extend some recent results in the literature.

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