Iterating Fixed Point via Generalized Mann’s Iteration in Convex b-Metric Spaces with Application

Iterating Fixed Point via Generalized Mann’s Iteration in Convex b-Metric Spaces with Application

This manuscript investigates fixed point of single-valued Hardy-Roger’s type F-contraction globally as well as locally in a convex b-metric space. The paper, using generalized Mann’s iteration, iterates fixed point of the abovementioned contraction; however, the third axiom (F3) of the F-contraction...

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Main Authors: A. Asif, M. Alansari, N. Hussain, M. Arshad, A. Ali
Format: Article
Language:English
Published: Hindawi-Wiley 2021-01-01
Series:Complexity
Online Access:http://dx.doi.org/10.1155/2021/8534239
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spelling doaj-3809c44ce83747f5ba3a67755fccd1622021-03-08T02:00:26ZengHindawi-WileyComplexity1099-05262021-01-01202110.1155/2021/8534239Iterating Fixed Point via Generalized Mann’s Iteration in Convex b-Metric Spaces with ApplicationA. Asif0M. Alansari1N. Hussain2M. Arshad3A. Ali4Department of Mathematics and StatisticsDepartment of MathematicsDepartment of MathematicsDepartment of Mathematics and StatisticsDepartment of Mathematics and StatisticsThis manuscript investigates fixed point of single-valued Hardy-Roger’s type F-contraction globally as well as locally in a convex b-metric space. The paper, using generalized Mann’s iteration, iterates fixed point of the abovementioned contraction; however, the third axiom (F3) of the F-contraction is removed, and thus the mapping F is relaxed. An important approach used in the article is, though a subset closed ball of a complete convex b-metric space is not necessarily complete, the convergence of the Cauchy sequence is confirmed in the subset closed ball. The results further lead us to some important corollaries, and examples are produced in support of our main theorems. The paper most importantly presents application of our results in finding solution to the integral equations.http://dx.doi.org/10.1155/2021/8534239
collection DOAJ
language English
format Article
sources DOAJ
author A. Asif
M. Alansari
N. Hussain
M. Arshad
A. Ali
spellingShingle A. Asif
M. Alansari
N. Hussain
M. Arshad
A. Ali
Iterating Fixed Point via Generalized Mann’s Iteration in Convex b-Metric Spaces with Application
Complexity
author_facet A. Asif
M. Alansari
N. Hussain
M. Arshad
A. Ali
author_sort A. Asif
title Iterating Fixed Point via Generalized Mann’s Iteration in Convex b-Metric Spaces with Application
title_short Iterating Fixed Point via Generalized Mann’s Iteration in Convex b-Metric Spaces with Application
title_full Iterating Fixed Point via Generalized Mann’s Iteration in Convex b-Metric Spaces with Application
title_fullStr Iterating Fixed Point via Generalized Mann’s Iteration in Convex b-Metric Spaces with Application
title_full_unstemmed Iterating Fixed Point via Generalized Mann’s Iteration in Convex b-Metric Spaces with Application
title_sort iterating fixed point via generalized mann’s iteration in convex b-metric spaces with application
publisher Hindawi-Wiley
series Complexity
issn 1099-0526
publishDate 2021-01-01
description This manuscript investigates fixed point of single-valued Hardy-Roger’s type F-contraction globally as well as locally in a convex b-metric space. The paper, using generalized Mann’s iteration, iterates fixed point of the abovementioned contraction; however, the third axiom (F3) of the F-contraction is removed, and thus the mapping F is relaxed. An important approach used in the article is, though a subset closed ball of a complete convex b-metric space is not necessarily complete, the convergence of the Cauchy sequence is confirmed in the subset closed ball. The results further lead us to some important corollaries, and examples are produced in support of our main theorems. The paper most importantly presents application of our results in finding solution to the integral equations.
url http://dx.doi.org/10.1155/2021/8534239
work_keys_str_mv AT aasif iteratingfixedpointviageneralizedmannsiterationinconvexbmetricspaceswithapplication
AT malansari iteratingfixedpointviageneralizedmannsiterationinconvexbmetricspaceswithapplication
AT nhussain iteratingfixedpointviageneralizedmannsiterationinconvexbmetricspaceswithapplication
AT marshad iteratingfixedpointviageneralizedmannsiterationinconvexbmetricspaceswithapplication
AT aali iteratingfixedpointviageneralizedmannsiterationinconvexbmetricspaceswithapplication
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