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 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 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 A Viscosity Iterative Algorithm Technique for Solving a General Equilibrium Problem System

2019 ◽  
Vol 50 (4) ◽  
pp. 391-408
Author(s):  
Mahdi Azhini ◽  
Masoumeh Cheraghi ◽  
Hamid reza Sahebi
Keyword(s):  
Hilbert Space ◽  
General Equilibrium ◽  
Equilibrium Problem ◽  
Iterative Algorithm ◽  
Equilibrium Problems ◽  
Recent Decade ◽  
Nonexpansive Semigroup ◽  
Numerical Examples ◽  
Common Solution ◽  
Iteration Methods

In the recent decade, a considerable number of Equilibrium problems havebeen solved successfully based on the iteration methods. In this paper, we suggest a viscosity iterative algorithm for nonexpansive semigroup in the framework  of Hilbert space. We  prove that, the sequence generated by this algorithm under the certain  conditions imposed on parameters  strongly convergence to a common solution of general equilibrium problem system. Results presented in this paper extend and unify the previously known  results announced by many other authors. Further, we give some numerical examples to justify our main results.

scholarly journals Approximations for Equilibrium Problems and Nonexpansive Semigroups

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Huan-chun Wu ◽  
Cao-zong Cheng
Keyword(s):  
Iterative Method ◽  
Strong Convergence ◽  
Hilbert Spaces ◽  
Convergence Theorem ◽  
Equilibrium Problems ◽  
Common Fixed Points ◽  
Common Element ◽  
Strong Convergence Theorem ◽  
Nonexpansive Semigroup ◽  
New Iterative Method

We introduce a new iterative method for finding a common element of the set of solutions of an equilibrium problem and the set of all common fixed points of a nonexpansive semigroup and prove the strong convergence theorem in Hilbert spaces. Our result extends the recent result of Zegeye and Shahzad (2013). In the last part of the paper, by the way, we point out that there is a slight flaw in the proof of the main result in Shehu's paper (2012) and perfect the proof.

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.

scholarly journals Modified CGLS iterative algorithm for solving the generalized Sylvester-conjugate matrix equation

Filomat ◽  
2020 ◽  
Vol 34 (4) ◽  
pp. 1329-1346
Author(s):  
Caiqin Song ◽  
Qing-Wen Wang
Keyword(s):  
Iterative Method ◽  
Least Squares ◽  
Iterative Algorithm ◽  
Matrix Equation ◽  
Inner Product ◽  
Frobenius Norm ◽  
Finite Convergence ◽  
Numerical Examples ◽  
Roundoff Errors ◽  
New Iterative Method

By introducing the real inner product, this paper offers an modified conjugate gradient least squares iterative algorithm (MCGLS)for solving the generalized Sylvester-conjugate matrix equation. The properties of this algorithm are discussed and the finite convergence of this algorithm is proven. This new iterative method can obtain the symmetric least squares Frobenius norm solution within finite iteration steps in the absence of roundoff errors. Finally, two numerical examples are offered to illustrate the effectiveness of the proposed algorithm.

A synthetic algorithm for families of demicontractive and nonexpansive mappings and equilibrium problems

Filomat ◽  
2017 ◽  
Vol 31 (19) ◽  
pp. 5891-5908
Author(s):  
Ali Abkara ◽  
Mohsen Shekarbaigia
Keyword(s):  
Fixed Points ◽  
Rate Of Convergence ◽  
Equilibrium Problem ◽  
Equilibrium Problems ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
Common Element ◽  
Numerical Examples ◽  
Demicontractive Mappings

We study the rate of convergence of a new synthetic algorithm for finding a common element of the set of solutions of an equilibrium problem and the set of common fixed points of a pair of nonexpansive mappings and two finite families of demicontractive mappings. We then provide some numerical examples to illustrate our main result and the proposed algorithm.

scholarly journals New Hybrid Steepest Descent Algorithms for Equilibrium Problem and Infinitely Many Strict Pseudo-Contractions in Hilbert Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Peichao Duan
Keyword(s):  
Variational Inequality ◽  
Iterative Method ◽  
Strong Convergence ◽  
Equilibrium Problem ◽  
Hilbert Spaces ◽  
Iterative Scheme ◽  
Common Element ◽  
Numerical Examples ◽  
Contractive Mappings ◽  
General Iterative Method

We propose an explicit iterative scheme for finding a common element of the set of fixed points of infinitely many strict pseudo-contractive mappings and the set of solutions of an equilibrium problem by the general iterative method, which solves the variational inequality. In the setting of real Hilbert spaces, strong convergence theorems are proved. The results presented in this paper improve and extend the corresponding results reported by some authors recently. Furthermore, two numerical examples are given to demonstrate the effectiveness of our iterative scheme.

Iterative algorithm for a split equilibrium problem and fixed problem for finite asymptotically nonexpansive mappings in Hlbert space

Filomat ◽  
2017 ◽  
Vol 31 (5) ◽  
pp. 1423-1434 ◽  
Author(s):  
Sheng Wang ◽  
Min Chen
Keyword(s):  
Equilibrium Problem ◽  
Iterative Algorithm ◽  
Nonexpansive Mappings ◽  
Common Element ◽  
Fixed Point Set ◽  
Split Equilibrium Problem ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
Point Set ◽  
The Common

In this paper, we propose an iterative algorithm for finding the common element of solution set of a split equilibrium problem and common fixed point set of a finite family of asymptotically nonexpansive mappings in Hilbert space. The strong convergence of this algorithm is proved.

scholarly journals A New Iterative Numerical Continuation Technique for Approximating the Solutions of Scalar Nonlinear Equations

2017 ◽  
Vol 2017 ◽  
pp. 1-21 ◽  
Author(s):  
Grégory Antoni
Keyword(s):  
Numerical Analysis ◽  
Iterative Method ◽  
Iterative Algorithm ◽  
Nonlinear Equations ◽  
Numerical Procedure ◽  
Approximate Solutions ◽  
Numerical Continuation ◽  
Stationary Type ◽  
Continuation Technique ◽  
New Iterative Method

The present study concerns the development of a new iterative method applied to a numerical continuation procedure for parameterized scalar nonlinear equations. Combining both a modified Newton’s technique and a stationary-type numerical procedure, the proposed method is able to provide suitable approximate solutions associated with scalar nonlinear equations. A numerical analysis of predictive capabilities of this new iterative algorithm is addressed, assessed, and discussed on some specific examples.

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