On Generalized Nonexpansive Maps in Banach Spaces
We introduce a very general class of generalized non-expansive maps. This new class of maps properly includes the class of Suzuki non-expansive maps, Reich–Suzuki type non-expansive maps, and generalized <inline-formula> <math display="inline"> <semantics> <mi>α<...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-07-01
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| Series: | Computation |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2079-3197/8/3/61 |
| _version_ | 1797563405494648832 |
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| author | Kifayat Ullah Junaid Ahmad Manuel de la Sen |
| author_facet | Kifayat Ullah Junaid Ahmad Manuel de la Sen |
| author_sort | Kifayat Ullah |
| collection | DOAJ |
| description | We introduce a very general class of generalized non-expansive maps. This new class of maps properly includes the class of Suzuki non-expansive maps, Reich–Suzuki type non-expansive maps, and generalized <inline-formula> <math display="inline"> <semantics> <mi>α</mi> </semantics> </math> </inline-formula>-non-expansive maps. We establish some basic properties and demiclosed principle for this class of maps. After this, we establish existence and convergence results for this class of maps in the context of uniformly convex Banach spaces and compare several well known iterative algorithms. |
| first_indexed | 2024-03-10T18:42:09Z |
| format | Article |
| id | doaj.art-0f73eff0bd954a45a015272a031a934b |
| institution | Directory Open Access Journal |
| issn | 2079-3197 |
| language | English |
| last_indexed | 2024-03-10T18:42:09Z |
| publishDate | 2020-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Computation |
| spelling | doaj.art-0f73eff0bd954a45a015272a031a934b2023-11-20T05:44:07ZengMDPI AGComputation2079-31972020-07-01836110.3390/computation8030061On Generalized Nonexpansive Maps in Banach SpacesKifayat Ullah0Junaid Ahmad1Manuel de la Sen2Department of Mathematics, University of Science and Technology, Bannu 28100, Khyber Pakhtunkhwa, PakistanDepartment of Mathematics, University of Science and Technology, Bannu 28100, Khyber Pakhtunkhwa, PakistanInstitute of Research and Development of Processes, University of the Basque Country, Campus of Leioa (Bizkaia), P.O. Box 644- Bilbao, Barrio Sarriena, 48940 Leioa, SpainWe introduce a very general class of generalized non-expansive maps. This new class of maps properly includes the class of Suzuki non-expansive maps, Reich–Suzuki type non-expansive maps, and generalized <inline-formula> <math display="inline"> <semantics> <mi>α</mi> </semantics> </math> </inline-formula>-non-expansive maps. We establish some basic properties and demiclosed principle for this class of maps. After this, we establish existence and convergence results for this class of maps in the context of uniformly convex Banach spaces and compare several well known iterative algorithms.https://www.mdpi.com/2079-3197/8/3/61generalized non-expansive mapdemiclosed principleuniformly convex Banach spacerate of convergenceBanach space |
| spellingShingle | Kifayat Ullah Junaid Ahmad Manuel de la Sen On Generalized Nonexpansive Maps in Banach Spaces Computation generalized non-expansive map demiclosed principle uniformly convex Banach space rate of convergence Banach space |
| title | On Generalized Nonexpansive Maps in Banach Spaces |
| title_full | On Generalized Nonexpansive Maps in Banach Spaces |
| title_fullStr | On Generalized Nonexpansive Maps in Banach Spaces |
| title_full_unstemmed | On Generalized Nonexpansive Maps in Banach Spaces |
| title_short | On Generalized Nonexpansive Maps in Banach Spaces |
| title_sort | on generalized nonexpansive maps in banach spaces |
| topic | generalized non-expansive map demiclosed principle uniformly convex Banach space rate of convergence Banach space |
| url | https://www.mdpi.com/2079-3197/8/3/61 |
| work_keys_str_mv | AT kifayatullah ongeneralizednonexpansivemapsinbanachspaces AT junaidahmad ongeneralizednonexpansivemapsinbanachspaces AT manueldelasen ongeneralizednonexpansivemapsinbanachspaces |