Common zero point for a finite family of inclusion problems of accretive mappings in Banach spaces

Optimization ◽  
2018 ◽  
Vol 67 (8) ◽  
pp. 1183-1196 ◽  
Author(s):  
Shih-sen Chang ◽  
Ching-Feng Wen ◽  
Jen-Chih Yao
Keyword(s):  
Banach Spaces ◽  
Zero Point ◽  
Finite Family ◽  
Common Zero ◽  
Inclusion Problems ◽  
Accretive Mappings

scholarly journals Three step algorithm for weighted resolvent average of a finite family of monotone operators

Filomat ◽  
2018 ◽  
Vol 32 (17) ◽  
pp. 6031-6043
Author(s):  
Malihe Bagheri ◽  
Mehdi Roohi
Keyword(s):  
Iterative Method ◽  
Strong Convergence ◽  
Zero Point ◽  
Monotone Operators ◽  
Finite Family ◽  
Common Zero ◽  
Numerical Examples ◽  
Step Algorithm

In this paper, we introduce a composite iterative method for finding a common zero point of weighted resolvent average of a finite family of monotone operators. Furthermore, the strong convergence of the proposed iterative method is established. Finally, our results are illustrated by some numerical examples.

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.

scholarly journals Existence and Strong Convergence Theorems for Generalized Mixed Equilibrium Problems of a Finite Family of Asymptotically Nonexpansive Mappings in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-21
Author(s):  
Rabian Wangkeeree ◽  
Hossein Dehghan ◽  
Pakkapon Preechasilp
Keyword(s):  
Strong Convergence ◽  
Equilibrium Problem ◽  
Banach Spaces ◽  
Nonexpansive Mappings ◽  
Finite Family ◽  
Generalized Mixed Equilibrium Problem ◽  
Mixed Equilibrium Problem ◽  
Asymptotically Nonexpansive ◽  
Generalized Mixed Equilibrium ◽  
Mixed Equilibrium

We first prove the existence of solutions for a generalized mixed equilibrium problem under the new conditions imposed on the given bifunction and introduce the algorithm for solving a common element in the solution set of a generalized mixed equilibrium problem and the common fixed point set of finite family of asymptotically nonexpansive mappings. Next, the strong convergence theorems are obtained, under some appropriate conditions, in uniformly convex and smooth Banach spaces. The main results extend various results existing in the current literature.

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