The method for solving fixed point problem of \(G\)-nonexpansive mapping in Hilbert spaces endowed with graphs and numerical example
type: Item
instance of: scholarly article
title: The method for solving fixed point problem of \(G\)-nonexpansive mapping in Hilbert spaces endowed with graphs and numerical example
zbMATH Open document ID: 1444.47075
author: Wongvisarut Khuangsatung
author: Atid Kangtunyakarn
published in: Indian Journal of Pure \& Applied Mathematics
publication date: 2020-04-07T00:00:00Z
review text: A new viscosity approximation method is employed to obtain a strong convergence theorem for finding the set of fixed points of a $G$-nonexpansive mapping in a Hilbert space endowed with a directed graph. The result generalizes some well-known results in the literature. A~numerical example is provided to support the claims, with some consequences of the obtained result given as remarks.
Mathematics Subject Classification ID: 47J26
Mathematics Subject Classification ID: 47H09
zbMATH DE Number: 7187885
zbMATH Keywords: \(G\)-nonexpansive mappings
zbMATH Keywords: viscosity approximation method
zbMATH Keywords: edge-preserving
zbMATH Keywords: strong convergence
zbMATH Keywords: Hilbert space
reviewed by: Adesanmi Alao Mogbademu
MaRDI profile type: Publication
full work available at URL: s13226-020-0391-y
OpenAlex ID: W3011356699
cites work: Q3009219
cites work: Fixed point theorems for Reich type contractions on metric spaces with a graph
cites work: Fixed points of Mizoguchi-Takahashi contraction on a metric space with a graph and applications
cites work: The contraction principle for set valued mappings on a metric space with a graph
cites work: Coupled coincidence point theorems for generalized nonlinear contraction in partially ordered metric spaces
cites work: Common fixed point theorems for weakly increasing mappings on ordered orbitally complete metric spaces
cites work: The contraction principle for mappings on a metric space with a graph
cites work: Coincidence point and fixed point theorems for a new type of \(G\)-contraction multivalued mappings on a metric space endowed with a graph
cites work: Coincidence point theorems for some multi-valued mappings in complete metric spaces endowed with a graph
cites work: Fixed point results for multivalued contractions on a metric space with a graph
cites work: Fixed points of monotone nonexpansive mappings with a graph
cites work: On Browder's convergence theorem and Halpern iteration process for \(G\)-nonexpansive mappings in Hilbert spaces endowed with graphs
cites work: Viscosity approximation methods for nonexpansive mappings
cites work: Viscosity approximation methods for fixed-points problems
cites work: Fixed Point Theory for Lipschitzian-type Mappings with Applications
cites work: An iterative approach to quadratic optimization
cites work: Nonlinear functional analysis. Fixed point theory and its applications
cites work: Weak convergence of the sequence of successive approximations for nonexpansive mappings
cites work: Dominating sets in directed graphs
cites work: The Computation of π to 29,360,000 Decimal Digits Using Borweins' Quartically Convergent Algorithm
cites work: Ramanujan, Modular Equations, and Approximations to Pi or How to Compute One Billion Digits of Pi
DOI: 10.1007/S13226-020-0391-Y
description: scientific article; zbMATH DE number 7187885