scholarly journals On Solutions of Variational Inequality Problems via Iterative Methods

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Mohammed Ali Alghamdi ◽  
Naseer Shahzad ◽  
Habtu Zegeye
Keyword(s):  
Variational Inequality ◽  
Fixed Points ◽  
Iterative Methods ◽  
Common Point ◽  
Finite Family ◽  
Variational Inequality Problems ◽  
Important Class ◽  
Pseudocontractive Mappings ◽  
Accretive Mappings ◽  
Nonlinear Mappings

We investigate an algorithm for a common point of fixed points of a finite family of Lipschitz pseudocontractive mappings and solutions of a finite family ofγ-inverse strongly accretive mappings. Our theorems improve and unify most of the results that have been proved in this direction for this important class of nonlinear mappings.

scholarly journals Solutions of variational inequality problems in the set of fixed points of pseudocontractive mappings

2014 ◽  
Vol 30 (2) ◽  
pp. 257-265
Author(s):  
HABTU ZEGEYE ◽  
◽  
NASSER SHAHZAD ◽  
Keyword(s):  
Variational Inequality ◽  
Fixed Points ◽  
Iterative Process ◽  
Variational Inequality Problems ◽  
Important Class ◽  
Nonlinear Operators ◽  
Pseudocontractive Mappings ◽  
Accretive Mappings

We introduce an iterative process which converges strongly to a solution of the variational inequality problems for η-inverse strongly accretive mappings in the set of fixed points of pseudocontractive mappings. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear operators.

scholarly journals Further Investigation on the Relaxed Hybrid Steepest-Descent Methods for Variational Inequalities withk-Strict Pseudocontractions

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Qian-Fen Gong ◽  
Dao-Jun Wen
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Fixed Points ◽  
Convergence Analysis ◽  
Common Fixed Points ◽  
Finite Family ◽  
Steepest Descent ◽  
Descent Methods ◽  
Pseudocontractive Mappings ◽  
Strictly Pseudocontractive Mappings

We modify the relaxed hybrid steepest-descent methods to the case of variational inequality for finding a solution over the set of common fixed points of a finite family of strictly pseudocontractive mappings. The strongly monotone property defined on cost operator was extended to relaxed cocoercive in convergence analysis. Results presented in this paper may be viewed as a refinement and important generalizations of the previously known results announced by many other authors.

scholarly journals A strong convergence theorem for a zero of the sum of a finite family of maximally monotone mappings

2020 ◽  
Vol 53 (1) ◽  
pp. 152-166 ◽  
Author(s):  
Getahun B. Wega ◽  
Habtu Zegeye ◽  
Oganeditse A. Boikanyo
Keyword(s):  
Strong Convergence ◽  
Approximation Method ◽  
Convergence Theorem ◽  
Finite Family ◽  
Strong Convergence Theorem ◽  
Monotone Mappings ◽  
Important Class ◽  
Numerical Example ◽  
Minimization Problems ◽  
Nonlinear Mappings

AbstractThe purpose of this article is to study the method of approximation for zeros of the sum of a finite family of maximally monotone mappings and prove strong convergence of the proposed approximation method under suitable conditions. The method of proof is of independent interest. In addition, we give some applications to the minimization problems and provide a numerical example which supports our main result. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear mappings.

scholarly journals Path Convergence and Approximation of Common Zeroes of a Finite Family ofm-Accretive Mappings in Banach Spaces

2010 ◽  
Vol 2010 ◽  
pp. 1-14 ◽  
Author(s):  
Yekini Shehu ◽  
Jerry N. Ezeora
Keyword(s):  
Real Banach Space ◽  
Iterative Scheme ◽  
Finite Family ◽  
Duality Mapping ◽  
Strong Convergence Theorem ◽  
Sunny Nonexpansive Retraction ◽  
Mild Conditions ◽  
Pseudocontractive Mappings ◽  
Uniformly Smooth ◽  
Accretive Mappings

LetEbe a real Banach space which is uniformly smooth and uniformly convex. LetKbe a nonempty, closed, and convex sunny nonexpansive retract ofE, whereQis the sunny nonexpansive retraction. IfEadmits weakly sequentially continuous duality mappingj, path convergence is proved for a nonexpansive mappingT:K→K. As an application, we prove strong convergence theorem for common zeroes of a finite family ofm-accretive mappings ofKtoE. As a consequence, an iterative scheme is constructed to converge to a common fixed point (assuming existence) of a finite family of pseudocontractive mappings fromKtoEunder certain mild conditions.

Sign in / Sign up

Export Citation Format

Share Document