Generalized Enriched Nonexpansive Mappings and Their Fixed Point Theorems
This paper introduces a novel category of nonlinear mappings and provides several theorems on their existence and convergence in Banach spaces, subject to various assumptions. Moreover, we obtain convergence theorems concerning iterates of α-Krasnosel’skiĭ mapping associated with the newly defined c...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2023-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2023/5572893 |
| _version_ | 1827077599335022592 |
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| author | Rahul Shukla Rekha Panicker |
| author_facet | Rahul Shukla Rekha Panicker |
| author_sort | Rahul Shukla |
| collection | DOAJ |
| description | This paper introduces a novel category of nonlinear mappings and provides several theorems on their existence and convergence in Banach spaces, subject to various assumptions. Moreover, we obtain convergence theorems concerning iterates of α-Krasnosel’skiĭ mapping associated with the newly defined class of mappings. Further, we present that α-Krasnosel’skiĭ mapping associated with b-enriched quasinonexpansive mapping is asymptotically regular. Furthermore, some new convergence theorems concerning b-enriched quasinonexpansive mappings have been proved. |
| first_indexed | 2024-03-09T01:30:44Z |
| format | Article |
| id | doaj.art-d9920fb6c76a4e20acce00789fd13393 |
| institution | Directory Open Access Journal |
| issn | 1687-0409 |
| language | English |
| last_indexed | 2025-03-20T02:16:20Z |
| publishDate | 2023-01-01 |
| publisher | Hindawi Limited |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj.art-d9920fb6c76a4e20acce00789fd133932024-10-03T07:51:53ZengHindawi LimitedAbstract and Applied Analysis1687-04092023-01-01202310.1155/2023/5572893Generalized Enriched Nonexpansive Mappings and Their Fixed Point TheoremsRahul Shukla0Rekha Panicker1Department of Mathematical Sciences and ComputingDepartment of Mathematical Sciences and ComputingThis paper introduces a novel category of nonlinear mappings and provides several theorems on their existence and convergence in Banach spaces, subject to various assumptions. Moreover, we obtain convergence theorems concerning iterates of α-Krasnosel’skiĭ mapping associated with the newly defined class of mappings. Further, we present that α-Krasnosel’skiĭ mapping associated with b-enriched quasinonexpansive mapping is asymptotically regular. Furthermore, some new convergence theorems concerning b-enriched quasinonexpansive mappings have been proved.http://dx.doi.org/10.1155/2023/5572893 |
| spellingShingle | Rahul Shukla Rekha Panicker Generalized Enriched Nonexpansive Mappings and Their Fixed Point Theorems Abstract and Applied Analysis |
| title | Generalized Enriched Nonexpansive Mappings and Their Fixed Point Theorems |
| title_full | Generalized Enriched Nonexpansive Mappings and Their Fixed Point Theorems |
| title_fullStr | Generalized Enriched Nonexpansive Mappings and Their Fixed Point Theorems |
| title_full_unstemmed | Generalized Enriched Nonexpansive Mappings and Their Fixed Point Theorems |
| title_short | Generalized Enriched Nonexpansive Mappings and Their Fixed Point Theorems |
| title_sort | generalized enriched nonexpansive mappings and their fixed point theorems |
| url | http://dx.doi.org/10.1155/2023/5572893 |
| work_keys_str_mv | AT rahulshukla generalizedenrichednonexpansivemappingsandtheirfixedpointtheorems AT rekhapanicker generalizedenrichednonexpansivemappingsandtheirfixedpointtheorems |