Iterative Construction of Fixed Points for Operators Endowed with Condition E in Metric Spaces

Iterative Construction of Fixed Points for Operators Endowed with Condition E in Metric Spaces

We consider the class of mappings endowed with the condition E in a nonlinear domain called 2-uniformly convex hyperbolic space. We provide some strong and Δ-convergence theorems for this class of mappings under the Agarwal iterative process. In order to support the main outcome, we procure an examp...

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Main Authors: Junaid Ahmad, Kifayat Ullah, Hüseyin Işik, Muhammad Arshad, Manuel de la Sen
Format: Article
Language:English
Published: Hindawi Limited 2021-01-01
Series:Advances in Mathematical Physics
Online Access:http://dx.doi.org/10.1155/2021/7930128
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spelling doaj-6e51de78f281488b9fa186866e1ea4552021-07-19T01:03:41ZengHindawi LimitedAdvances in Mathematical Physics1687-91392021-01-01202110.1155/2021/7930128Iterative Construction of Fixed Points for Operators Endowed with Condition E in Metric SpacesJunaid Ahmad0Kifayat Ullah1Hüseyin Işik2Muhammad Arshad3Manuel de la Sen4Department of Mathematics and StatisticsDepartment of MathematicsDepartment of Engineering ScienceDepartment of Mathematics and StatisticsInstitute of Research and Development of ProcessesWe consider the class of mappings endowed with the condition E in a nonlinear domain called 2-uniformly convex hyperbolic space. We provide some strong and Δ-convergence theorems for this class of mappings under the Agarwal iterative process. In order to support the main outcome, we procure an example of mappings endowed with the condition E and prove that its Agarwal iterative process is more effective than Mann and Ishikawa iterative processes. Simultaneously, our results hold in uniformly convex Banach, CAT(0), and some CAT(κ) spaces. This approach essentially provides a new setting for researchers who are working on the iterative procedures in fixed point theory and applications.http://dx.doi.org/10.1155/2021/7930128
collection DOAJ
language English
format Article
sources DOAJ
author Junaid Ahmad
Kifayat Ullah
Hüseyin Işik
Muhammad Arshad
Manuel de la Sen
spellingShingle Junaid Ahmad
Kifayat Ullah
Hüseyin Işik
Muhammad Arshad
Manuel de la Sen
Iterative Construction of Fixed Points for Operators Endowed with Condition E in Metric Spaces
Advances in Mathematical Physics
author_facet Junaid Ahmad
Kifayat Ullah
Hüseyin Işik
Muhammad Arshad
Manuel de la Sen
author_sort Junaid Ahmad
title Iterative Construction of Fixed Points for Operators Endowed with Condition E in Metric Spaces
title_short Iterative Construction of Fixed Points for Operators Endowed with Condition E in Metric Spaces
title_full Iterative Construction of Fixed Points for Operators Endowed with Condition E in Metric Spaces
title_fullStr Iterative Construction of Fixed Points for Operators Endowed with Condition E in Metric Spaces
title_full_unstemmed Iterative Construction of Fixed Points for Operators Endowed with Condition E in Metric Spaces
title_sort iterative construction of fixed points for operators endowed with condition e in metric spaces
publisher Hindawi Limited
series Advances in Mathematical Physics
issn 1687-9139
publishDate 2021-01-01
description We consider the class of mappings endowed with the condition E in a nonlinear domain called 2-uniformly convex hyperbolic space. We provide some strong and Δ-convergence theorems for this class of mappings under the Agarwal iterative process. In order to support the main outcome, we procure an example of mappings endowed with the condition E and prove that its Agarwal iterative process is more effective than Mann and Ishikawa iterative processes. Simultaneously, our results hold in uniformly convex Banach, CAT(0), and some CAT(κ) spaces. This approach essentially provides a new setting for researchers who are working on the iterative procedures in fixed point theory and applications.
url http://dx.doi.org/10.1155/2021/7930128
work_keys_str_mv AT junaidahmad iterativeconstructionoffixedpointsforoperatorsendowedwithconditioneinmetricspaces
AT kifayatullah iterativeconstructionoffixedpointsforoperatorsendowedwithconditioneinmetricspaces
AT huseyinisik iterativeconstructionoffixedpointsforoperatorsendowedwithconditioneinmetricspaces
AT muhammadarshad iterativeconstructionoffixedpointsforoperatorsendowedwithconditioneinmetricspaces
AT manueldelasen iterativeconstructionoffixedpointsforoperatorsendowedwithconditioneinmetricspaces
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