On Iteration <i>S</i><sub>n</sub> for Operators with Condition (D)

On Iteration <i>S</i><sub>n</sub> for Operators with Condition (D)

A recently introduced nonexpansive-type condition is subjected to an in-depth analysis. New examples are provided to highlight the relationship with Suzuki-type mappings. Furthermore, a convergence survey is conducted based on the iteration procedure <inline-formula><math display="inli...

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Bibliographic Details
Main Authors: Cristian Ciobanescu, Teodor Turcanu
Format: Article
Language:English
Published: MDPI AG 2020-10-01
Series:Symmetry
Subjects:
nonexpansive mapping
Suzuki mapping
condition (D)
Opial property
iteration procedure
convergence
Online Access:https://www.mdpi.com/2073-8994/12/10/1676
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spelling doaj-b033b81784374bb3865618c0cc2e39972020-11-25T03:53:56ZengMDPI AGSymmetry2073-89942020-10-01121676167610.3390/sym12101676On Iteration <i>S</i><sub>n</sub> for Operators with Condition (D)Cristian Ciobanescu0Teodor Turcanu1Department of Mathematics and Informatics, University Politehnica of Bucharest, 060042 Bucharest, RomaniaDepartment of Mathematics and Informatics, University Politehnica of Bucharest, 060042 Bucharest, RomaniaA recently introduced nonexpansive-type condition is subjected to an in-depth analysis. New examples are provided to highlight the relationship with Suzuki-type mappings. Furthermore, a convergence survey is conducted based on the iteration procedure <inline-formula><math display="inline"><semantics><msub><mi>S</mi><mi>n</mi></msub></semantics></math></inline-formula>. Issues related to data dependence and the stability of this iterative process are also being studied. Our study is performed in the framework of Banach spaces, in which the symmetry of the associated metric is a fundamental axiom and plays a key role while proving many results of this paper.https://www.mdpi.com/2073-8994/12/10/1676nonexpansive mappingSuzuki mappingcondition (D)Opial propertyiteration procedureconvergence
collection DOAJ
language English
format Article
sources DOAJ
author Cristian Ciobanescu
Teodor Turcanu
spellingShingle Cristian Ciobanescu
Teodor Turcanu
On Iteration <i>S</i><sub>n</sub> for Operators with Condition (D)
Symmetry
nonexpansive mapping
Suzuki mapping
condition (D)
Opial property
iteration procedure
convergence
author_facet Cristian Ciobanescu
Teodor Turcanu
author_sort Cristian Ciobanescu
title On Iteration <i>S</i><sub>n</sub> for Operators with Condition (D)
title_short On Iteration <i>S</i><sub>n</sub> for Operators with Condition (D)
title_full On Iteration <i>S</i><sub>n</sub> for Operators with Condition (D)
title_fullStr On Iteration <i>S</i><sub>n</sub> for Operators with Condition (D)
title_full_unstemmed On Iteration <i>S</i><sub>n</sub> for Operators with Condition (D)
title_sort on iteration <i>s</i><sub>n</sub> for operators with condition (d)
publisher MDPI AG
series Symmetry
issn 2073-8994
publishDate 2020-10-01
description A recently introduced nonexpansive-type condition is subjected to an in-depth analysis. New examples are provided to highlight the relationship with Suzuki-type mappings. Furthermore, a convergence survey is conducted based on the iteration procedure <inline-formula><math display="inline"><semantics><msub><mi>S</mi><mi>n</mi></msub></semantics></math></inline-formula>. Issues related to data dependence and the stability of this iterative process are also being studied. Our study is performed in the framework of Banach spaces, in which the symmetry of the associated metric is a fundamental axiom and plays a key role while proving many results of this paper.
topic nonexpansive mapping
Suzuki mapping
condition (D)
Opial property
iteration procedure
convergence
url https://www.mdpi.com/2073-8994/12/10/1676
work_keys_str_mv AT cristianciobanescu oniterationisisubnsubforoperatorswithconditiond
AT teodorturcanu oniterationisisubnsubforoperatorswithconditiond
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