A Common Fixed Point Theorem Using an Iterative Method

A Common Fixed Point Theorem Using an Iterative Method

Let $ H$ be a Hilbert space and $C$ be a closed, convex and nonempty subset of $H$. Let $T:C rightarrow H$ be a non-self and non-expansive mapping. V. Colao and G. Marino with particular choice of the sequence  ${alpha_{n}}$ in Krasonselskii-Mann algorithm, ${x}_{n+1}={alpha}_{n}{x}_{n}+(1-{alpha}_{...

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Main Author: Ali Bagheri Vakilabad
Format: Article
Language:English
Published: University of Maragheh 2020-01-01
Series:Sahand Communications in Mathematical Analysis
Subjects:
hilbert space
nonexpansive mapping
krasnoselskii-mann iterative method
inward condition
Online Access:http://scma.maragheh.ac.ir/article_37370_23b71732cb85f46fa137d11f68350735.pdf
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spelling doaj-4beb7f1577764cecae0194a6bdba38082020-11-25T03:48:41ZengUniversity of MaraghehSahand Communications in Mathematical Analysis2322-58072423-39002020-01-01171919810.22130/scma.2019.71435.28137370A Common Fixed Point Theorem Using an Iterative MethodAli Bagheri Vakilabad0Department of Mathematics, Ardabil Branch, Islamic Azad University, Ardabil, Iran.Let $ H$ be a Hilbert space and $C$ be a closed, convex and nonempty subset of $H$. Let $T:C rightarrow H$ be a non-self and non-expansive mapping. V. Colao and G. Marino with particular choice of the sequence  ${alpha_{n}}$ in Krasonselskii-Mann algorithm, ${x}_{n+1}={alpha}_{n}{x}_{n}+(1-{alpha}_{n})T({x}_{n}),$ proved both weak and strong converging results. In this paper, we generalize their algorithm and result, imposing some conditions upon the set $C$ and finite many mappings from $C$ in to $H$, to obtain a converging sequence to a common fixed point for these non-self and non-expansive mappings.http://scma.maragheh.ac.ir/article_37370_23b71732cb85f46fa137d11f68350735.pdfhilbert spacenonexpansive mappingkrasnoselskii-mann iterative methodinward condition
collection DOAJ
language English
format Article
sources DOAJ
author Ali Bagheri Vakilabad
spellingShingle Ali Bagheri Vakilabad
A Common Fixed Point Theorem Using an Iterative Method
Sahand Communications in Mathematical Analysis
hilbert space
nonexpansive mapping
krasnoselskii-mann iterative method
inward condition
author_facet Ali Bagheri Vakilabad
author_sort Ali Bagheri Vakilabad
title A Common Fixed Point Theorem Using an Iterative Method
title_short A Common Fixed Point Theorem Using an Iterative Method
title_full A Common Fixed Point Theorem Using an Iterative Method
title_fullStr A Common Fixed Point Theorem Using an Iterative Method
title_full_unstemmed A Common Fixed Point Theorem Using an Iterative Method
title_sort common fixed point theorem using an iterative method
publisher University of Maragheh
series Sahand Communications in Mathematical Analysis
issn 2322-5807
2423-3900
publishDate 2020-01-01
description Let $ H$ be a Hilbert space and $C$ be a closed, convex and nonempty subset of $H$. Let $T:C rightarrow H$ be a non-self and non-expansive mapping. V. Colao and G. Marino with particular choice of the sequence  ${alpha_{n}}$ in Krasonselskii-Mann algorithm, ${x}_{n+1}={alpha}_{n}{x}_{n}+(1-{alpha}_{n})T({x}_{n}),$ proved both weak and strong converging results. In this paper, we generalize their algorithm and result, imposing some conditions upon the set $C$ and finite many mappings from $C$ in to $H$, to obtain a converging sequence to a common fixed point for these non-self and non-expansive mappings.
topic hilbert space
nonexpansive mapping
krasnoselskii-mann iterative method
inward condition
url http://scma.maragheh.ac.ir/article_37370_23b71732cb85f46fa137d11f68350735.pdf
work_keys_str_mv AT alibagherivakilabad acommonfixedpointtheoremusinganiterativemethod
AT alibagherivakilabad commonfixedpointtheoremusinganiterativemethod
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