scholarly journals A viscosity iterative algorithm for the optimization problem system

Filomat ◽  
2017 ◽  
Vol 31 (8) ◽  
pp. 2249-2266 ◽  
Author(s):  
H.R. Sahebi ◽  
S. Ebrahimi
Keyword(s):  
Variational Inequality ◽  
Fixed Points ◽  
Equilibrium Problem ◽  
Iterative Algorithm ◽  
Optimization Problem ◽  
Common Fixed Points ◽  
Numerical Results ◽  
Common Element ◽  
Nonexpansive Semigroup ◽  
Mixed Equilibrium Problem

In this paper, we suggest and analysis a viscosity iterative algorithm for finding a common element of the set of solution of a mixed equilibrium problem and the set the of solutions of a variational inequality and all common fixed points of a nonexpansive semigroup. This algorithm strongly converges to an element which solves an optimization problem system. Finally, some examples and numerical results are also given.

scholarly journals An explicit viscosity iterative algorithm for finding the solutions of a general equilibrium problem systems

2015 ◽  
Vol 46 (3) ◽  
pp. 193-216
Author(s):  
H. R. Sahebi ◽  
S. Ebrahimi
Keyword(s):  
General Equilibrium ◽  
Fixed Points ◽  
Equilibrium Problem ◽  
Iterative Algorithm ◽  
Convex Subset ◽  
Common Element ◽  
Nonexpansive Semigroup ◽  
Matlab Software ◽  
Numerical Examples

We suggest an explicit viscosity iterative algorithm for finding a common element of the set of solutions for an general equilibrium problem system (GEPS) involving a bifunction defined on a closed, convex subset and the set of fixed points of a nonexpansive semigroup on another one in Hilbert's spaces. Furthermore, we present some numerical examples(by using MATLAB software) to guarantee the main result of this paper.

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

Filomat ◽  
2014 ◽  
Vol 28 (7) ◽  
pp. 1393-1415 ◽  
Author(s):  
H.R. Sahebi ◽  
A. Razani
Keyword(s):  
Iterative Method ◽  
General Equilibrium ◽  
Fixed Points ◽  
Equilibrium Problem ◽  
Iterative Algorithm ◽  
Common Element ◽  
Nonexpansive Semigroup ◽  
Numerical Examples ◽  
New Iterative Method

In this paper, we introduce a new iterative method for finding a common element of the set of solution of a general equilibrium problem system (GEPS) and the set of fixed points of a nonexpansive semigroup. Furthermore, we present some numerical examples (by using MATLsoftware) to guarantee the main result of this paper.

scholarly journals Convergence Theorem for Equilibrium and Variational Inequality Problems and a Family of Infinitely Nonexpansive Mappings in Hilbert Space

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Zhou Yinying ◽  
Cao Jiantao ◽  
Wang Yali
Keyword(s):  
Hilbert Space ◽  
Variational Inequality ◽  
Strong Convergence ◽  
Fixed Points ◽  
Equilibrium Problem ◽  
Convergence Theorem ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
Common Element

We introduce a hybrid iterative scheme for finding a common element of the set of common fixed points for a family of infinitely nonexpansive mappings, the set of solutions of the varitional inequality problem and the equilibrium problem in Hilbert space. Under suitable conditions, some strong convergence theorems are obtained. Our results improve and extend the corresponding results in (Chang et al. (2009), Min and Chang (2012), Plubtieng and Punpaeng (2007), S. Takahashi and W. Takahashi (2007), Tada and Takahashi (2007), Gang and Changsong (2009), Ying (2013), Y. Yao and J. C. Yao (2007), and Yong-Cho and Kang (2012)).

scholarly journals A new Halpern-type algorithm for a generalized mixed equilibrium problem and a countable family of generalized nonexpansive-type maps

2018 ◽  
Vol 34 (2) ◽  
pp. 191-198
Author(s):  
C. E. CHIDUME ◽  
◽  
M. O. NNAKWE ◽  
Keyword(s):  
Equilibrium Problem ◽  
Hilbert Spaces ◽  
Common Fixed Points ◽  
Countable Family ◽  
Generalized Mixed Equilibrium Problem ◽  
Common Element ◽  
Mixed Equilibrium Problem ◽  
Uniformly Smooth ◽  
Generalized Mixed Equilibrium ◽  
Mixed Equilibrium

Let K be a nonempty closed and convex subset of a uniformly smooth and uniformly convex real Banach space with dual space E∗. In this paper, a new iterative algorithm of Halpern-type is constructed and used to approximate a common element of a generalized mixed equilibrium problem and a common fixed points for a countable family of generalized nonexpansive-type maps. Application of our theorem, in the case of real Hilbert spaces, complements, extends and improves several important recent results. Finally, we give numerical experiments to illustrate the convergence of our sequence.

scholarly journals Algorithms of common solutions for a fixed point of hemicontractive-type mapping and a generalized equilibrium problem

2017 ◽  
Vol 5 (1) ◽  
pp. 20
Author(s):  
Habtu Zegeye ◽  
Tesfalem Hadush Meche ◽  
Mengistu Goa Sangago
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Equilibrium Problem ◽  
Iterative Algorithm ◽  
Hilbert Spaces ◽  
Research Area ◽  
Common Element ◽  
Generalized Equilibrium Problem ◽  
Type Mapping ◽  
Generalized Equilibrium

In this paper, we introduce and study an iterative algorithm for finding a common element of the set of fixed points of a Lipschitz hemicontractive-type multi-valued mapping and the set of solutions of a generalized equilibrium problem in the framework of Hilbert spaces. Our results improve and extend most of the results that have been proved previously by many authors in this research area.

Sign in / Sign up

Export Citation Format

Share Document