Strong convergence theorem for a finite family of demimetric mappings with variational inequality problems in a Hilbert space

2017 ◽  
Vol 34 (1) ◽  
pp. 41-57 ◽  
Author(s):  
Wataru Takahashi
Keyword(s):  
Hilbert Space ◽  
Variational Inequality ◽  
Strong Convergence ◽  
Convergence Theorem ◽  
Finite Family ◽  
Variational Inequality Problems ◽  
Strong Convergence Theorem

A new self adaptive Tseng’s extragradient method with double-projection for solving pseudomonotone variational inequality problems in Hilbert spaces

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Zhongbing Xie ◽  
Gang Cai ◽  
Xiaoxiao Li ◽  
Qiao-Li Dong
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Strong Convergence ◽  
Hilbert Spaces ◽  
Convergence Theorem ◽  
Numerical Experiments ◽  
Extragradient Method ◽  
Variational Inequality Problems ◽  
Strong Convergence Theorem ◽  
Tseng’S Extragradient Method

Abstract The purpose of this paper is to study a new Tseng’s extragradient method with two different stepsize rules for solving pseudomonotone variational inequalities in real Hilbert spaces. We prove a strong convergence theorem of the proposed algorithm under some suitable conditions imposed on the parameters. Moreover, we also give some numerical experiments to demonstrate the performance of our algorithm.

scholarly journals Approximation of Common Fixed Points of a Sequence of Nearly Nonexpansive Mappings and Solutions of Variational Inequality Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
D. R. Sahu ◽  
Shin Min Kang ◽  
Vidya Sagar
Keyword(s):  
Hilbert Space ◽  
Variational Inequality ◽  
Strong Convergence ◽  
Convergence Theorem ◽  
Variational Inequality Problem ◽  
Iterative Scheme ◽  
Real Hilbert Space ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
Strong Convergence Theorem

We introduce an explicit iterative scheme for computing a common fixed point of a sequence of nearly nonexpansive mappings defined on a closed convex subset of a real Hilbert space which is also a solution of a variational inequality problem. We prove a strong convergence theorem for a sequence generated by the considered iterative scheme under suitable conditions. Our strong convergence theorem extends and improves several corresponding results in the context of nearly nonexpansive mappings.

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.

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