Fixed points of weakly K-nonexpansive mappings and a stability result for fixed point iterative process with an application
Abstract In this article, we introduce a new type of non-expansive mapping, namely weakly K-nonexpansive mapping, which is weaker than non-expansiveness and stronger than quasi-nonexpansiveness. We prove some weak and strong convergence results using weakly K-nonexpansive mappings. Also, we define w...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-07-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13660-022-02826-9 |
| _version_ | 1811323681914224640 |
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| author | Sayantan Panja Kushal Roy Marija V. Paunović Mantu Saha Vahid Parvaneh |
| author_facet | Sayantan Panja Kushal Roy Marija V. Paunović Mantu Saha Vahid Parvaneh |
| author_sort | Sayantan Panja |
| collection | DOAJ |
| description | Abstract In this article, we introduce a new type of non-expansive mapping, namely weakly K-nonexpansive mapping, which is weaker than non-expansiveness and stronger than quasi-nonexpansiveness. We prove some weak and strong convergence results using weakly K-nonexpansive mappings. Also, we define weakly ( α , K ) $(\alpha ,K)$ -nonexpansive mapping and using it prove one stability result for JF-iterative process. Some prominent examples are presented illustrating the facts. A numerical example is given to compare the convergence behavior of some known iterative algorithms for weakly K-nonexpansive mappings. Moreover, we show by example that the class of α-nonexpansive mappings due to Aoyama and Kohsaka and the class of generalized α-nonexpansive mappings due to Pant and Shukla are independent. Finally, our fixed point theorem is applied to obtain a solution of a nonlinear fractional differential equation. |
| first_indexed | 2024-04-13T13:59:30Z |
| format | Article |
| id | doaj.art-2f5ca9a6b56f48c393e04896d8bc0ef5 |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-04-13T13:59:30Z |
| publishDate | 2022-07-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-2f5ca9a6b56f48c393e04896d8bc0ef52022-12-22T02:44:05ZengSpringerOpenJournal of Inequalities and Applications1029-242X2022-07-012022111810.1186/s13660-022-02826-9Fixed points of weakly K-nonexpansive mappings and a stability result for fixed point iterative process with an applicationSayantan Panja0Kushal Roy1Marija V. Paunović2Mantu Saha3Vahid Parvaneh4Department of Mathematics, The University of BurdwanDepartment of Mathematics, The University of BurdwanFaculty of Hotel Management and Tourism, University of KragujevacDepartment of Mathematics, The University of BurdwanDepartment of Mathematics, Gilan-E-Gharb Branch, Islamic Azad UniversityAbstract In this article, we introduce a new type of non-expansive mapping, namely weakly K-nonexpansive mapping, which is weaker than non-expansiveness and stronger than quasi-nonexpansiveness. We prove some weak and strong convergence results using weakly K-nonexpansive mappings. Also, we define weakly ( α , K ) $(\alpha ,K)$ -nonexpansive mapping and using it prove one stability result for JF-iterative process. Some prominent examples are presented illustrating the facts. A numerical example is given to compare the convergence behavior of some known iterative algorithms for weakly K-nonexpansive mappings. Moreover, we show by example that the class of α-nonexpansive mappings due to Aoyama and Kohsaka and the class of generalized α-nonexpansive mappings due to Pant and Shukla are independent. Finally, our fixed point theorem is applied to obtain a solution of a nonlinear fractional differential equation.https://doi.org/10.1186/s13660-022-02826-9Weakly K-nonexpansive and weakly ( α , K ) $(\alpha ,K)$ -nonexpansive mappingsSuzuki’s Condition (C)Generalized α-nonexpansive mappingStrong and weak convergence theoremsStability resultJF-iterative scheme |
| spellingShingle | Sayantan Panja Kushal Roy Marija V. Paunović Mantu Saha Vahid Parvaneh Fixed points of weakly K-nonexpansive mappings and a stability result for fixed point iterative process with an application Journal of Inequalities and Applications Weakly K-nonexpansive and weakly ( α , K ) $(\alpha ,K)$ -nonexpansive mappings Suzuki’s Condition (C) Generalized α-nonexpansive mapping Strong and weak convergence theorems Stability result JF-iterative scheme |
| title | Fixed points of weakly K-nonexpansive mappings and a stability result for fixed point iterative process with an application |
| title_full | Fixed points of weakly K-nonexpansive mappings and a stability result for fixed point iterative process with an application |
| title_fullStr | Fixed points of weakly K-nonexpansive mappings and a stability result for fixed point iterative process with an application |
| title_full_unstemmed | Fixed points of weakly K-nonexpansive mappings and a stability result for fixed point iterative process with an application |
| title_short | Fixed points of weakly K-nonexpansive mappings and a stability result for fixed point iterative process with an application |
| title_sort | fixed points of weakly k nonexpansive mappings and a stability result for fixed point iterative process with an application |
| topic | Weakly K-nonexpansive and weakly ( α , K ) $(\alpha ,K)$ -nonexpansive mappings Suzuki’s Condition (C) Generalized α-nonexpansive mapping Strong and weak convergence theorems Stability result JF-iterative scheme |
| url | https://doi.org/10.1186/s13660-022-02826-9 |
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