Approximating common fixed points of an evolution family on a metric space via Mann iteration
type: Item
instance of: scholarly article
title: Approximating common fixed points of an evolution family on a metric space via Mann iteration
zbMATH Open document ID: 1480.47075
DOI: 10.1155/2021/6764280
author: Liang Luo
author: Rizwan Ullah
author: Gul Rahmat
author: S. I. Butt
author: Muhammad Numan
published in: Journal of Mathematics
publication date: 2021-06-22T00:00:00Z
review text: Summary: In this article, we present the set of all common fixed points of a subfamily of an evolution family in terms of intersection of all common fixed points of only two operators from the family; that is, for subset \(\mathfrak{M}\) of \(\mathfrak{L} \), we have \(F(\mathfrak{M})= F(\mathfrak{Y}^{(\varrho_1,0)}) \cap F(\mathfrak{Y}^{(\varrho_2,0)})\), where \(\varrho_1\) and \(\varrho_2\) are positive and \((\varrho_1/\varrho_2)\) is an irrational number. Furthermore, we approximate such common fixed points by using the modified Mann iteration process. In fact, we are generalizing the results from a semigroup of operators to evolution families of operators on a metric space.
Mathematics Subject Classification ID: 47H20
Mathematics Subject Classification ID: 47H09
Mathematics Subject Classification ID: 47J26
Mathematics Subject Classification ID: 54H25
Mathematics Subject Classification ID: 54E40
zbMATH DE Number: 7361872
zbMATH Keywords: common fixed points
zbMATH Keywords: evolution family
zbMATH Keywords: modified Mann's iteration
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2021/6764280
OpenAlex ID: W3135990989
cites work: Handbook of metric fixed point theory
cites work: Fixed-point theorems for families of contraction mappings
cites work: Nonexpansive mappings and fixed-points in Banach spaces
cites work: NONEXPANSIVE NONLINEAR OPERATORS IN A BANACH SPACE
cites work: Properties of Fixed-Point Sets of Nonexpansive Mappings in Banach Spaces
cites work: A fixed point theorem for families of nonexpansive mappings
cites work: Common fixed points for commuting contraction mappings
cites work: An ergodic theorem for nonlinear semigroups of Lipschitzian mappings in Banach spaces
cites work: Approximate fixed point sequences of an evolution family on a metric space
cites work: On common fixed points in modular vector spaces
cites work: Q3188481
cites work: Approximating common fixed points of semigroups in metric spaces
cites work: On asymptotic pointwise contractions in modular function spaces
cites work: On asymptotic pointwise nonexpansive mappings in modular function spaces
cites work: Asymptotic pointwise contractions
cites work: On asymptotic pointwise contractions in metric spaces
cites work: Nonexpansive iterations in hyperbolic spaces
cites work: Uniform convexity of the hyperbolic metric and fixed points of holomorphic mappings in the Hilbert ball
cites work: Q3322631
cites work: On Metric Spaces with Uniform Normal Structure
cites work: The set of common fixed points of a one-parameter continuous semigroup of mappings is 𝐹\big(𝑇(1)\big)∩𝐹\big(𝑇(√2)\big)
cites work: Q3913946
cites work: Approximating common fixed points in hyperbolic spaces
cites work: Zum Prinzip der kontraktiven Abbildung
cites work: Common fixed points of a subfamily of a nonexpansive periodic evolution family on a strictly convex Banach space
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description: scientific article; zbMATH DE number 7361872