An iterative method for finding common solution of the fixed point problem of a finite family of nonexpansive mappings and a finite family of variational inequality problems in Hilbert space
type: Item
instance of: scholarly article
title: An iterative method for finding common solution of the fixed point problem of a finite family of nonexpansive mappings and a finite family of variational inequality problems in Hilbert space
zbMATH Open document ID: 1448.47071
DOI: 10.1155/2019/6875789
author: Shamshad Husain
author: Nisha Singh
published in: Journal of Applied Mathematics
publication date: 2019-05-07T00:00:00Z
review text: Summary: In this paper, a hybrid iterative algorithm is proposed for finding a common element of the set of common fixed points of finite family of nonexpansive mappings and the set of common solutions of the variational inequality for an inverse strongly monotone mapping on the real Hilbert space. We establish the strong convergence of the proposed method for approximating a common element of the above defined sets under some suitable conditions. The results presented in this paper extend and improve some well-known corresponding results in the earlier and recent literature.
Mathematics Subject Classification ID: 47J26
Mathematics Subject Classification ID: 47H09
Mathematics Subject Classification ID: 49J40
zbMATH DE Number: 7051375
zbMATH Keywords: hybrid iterative algorithm
zbMATH Keywords: real Hilbert space
zbMATH Keywords: strong convergence
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2019/6875789
OpenAlex ID: W2912117577
cites work: Pseudomonotone Complementarity Problems and Variational Inequalities
cites work: Iterative algorithm for generalized set-valued strongly nonlinear mixed variational-like inequali\-ties
cites work: Q5890172
cites work: Q4110807
cites work: Weak convergence theorems for nonexpansive mappings and monotone mappings
cites work: Strong convergence theorems for nonexpansive mappings and inverse-strongly monotone mappings
cites work: A general iterative method for nonexpansive mappings in Hilbert spaces
cites work: Convergence of a general iterative method for nonexpansive mappings in Hilbert spaces
cites work: The hybrid steepest descent method for the variational inequality problem over the intersection of fixed point sets of nonexpansive mappings
cites work: Viscosity approximation methods for fixed-points problems
cites work: Iterative methods for strict pseudo-contractions in Hilbert spaces
cites work: Viscosity approximation methods for nonexpansive mappings
cites work: Q3998720
cites work: On the Maximality of Sums of Nonlinear Monotone Operators
Wikidata QID: Q128532261
description: scientific article; zbMATH DE number 7051375