Shrinking Cesáro means method for the split equilibrium and fixed point problems in Hilbert spaces
Abstract We propose a modified version of the classical Cesáro means method endowed with the hybrid shrinking projection method to solve the split equilibrium and fixed point problems (SEFPP) in Hilbert spaces. One of the main reasons to equip the classical Cesáro means method with the shrinking pro...
| Main Authors: | , , , , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-07-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-020-02800-z |
| _version_ | 1811340080923541504 |
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| author | Samy A. Harisa M. A. A. Khan F. Mumtaz Nashat Faried Ahmed Morsy Kottakkaran Sooppy Nisar Abdul Ghaffar |
| author_facet | Samy A. Harisa M. A. A. Khan F. Mumtaz Nashat Faried Ahmed Morsy Kottakkaran Sooppy Nisar Abdul Ghaffar |
| author_sort | Samy A. Harisa |
| collection | DOAJ |
| description | Abstract We propose a modified version of the classical Cesáro means method endowed with the hybrid shrinking projection method to solve the split equilibrium and fixed point problems (SEFPP) in Hilbert spaces. One of the main reasons to equip the classical Cesáro means method with the shrinking projection method is to establish strong convergence results which are often required in infinite-dimensional functional spaces. As a consequence, the convergence analysis is carried out under mild conditions on the underlying shrinking Cesáro means method. We emphasize that the results accounted in this manuscript can be considered as an improvement and generalization of various existing exciting results in this field of study. |
| first_indexed | 2024-04-13T18:37:02Z |
| format | Article |
| id | doaj.art-678870d3ecd5446da8894ef53447f023 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-04-13T18:37:02Z |
| publishDate | 2020-07-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-678870d3ecd5446da8894ef53447f0232022-12-22T02:34:51ZengSpringerOpenAdvances in Difference Equations1687-18472020-07-012020111910.1186/s13662-020-02800-zShrinking Cesáro means method for the split equilibrium and fixed point problems in Hilbert spacesSamy A. Harisa0M. A. A. Khan1F. Mumtaz2Nashat Faried3Ahmed Morsy4Kottakkaran Sooppy Nisar5Abdul Ghaffar6Department of Mathematics, College of Arts and Sciences, Prince Sattam bin Abdulaziz UniversityDepartment of Mathematics, COMSATS University IslamabadDepartment of Mathematics, COMSATS University IslamabadDepartment of Mathematics, Faculty of Science, Ain Shams UniversityDepartment of Mathematics, College of Arts and Sciences, Prince Sattam bin Abdulaziz UniversityDepartment of Mathematics, College of Arts and Sciences, Prince Sattam bin Abdulaziz UniversityInformetrics Research Group, Ton Duc Thang UniversityAbstract We propose a modified version of the classical Cesáro means method endowed with the hybrid shrinking projection method to solve the split equilibrium and fixed point problems (SEFPP) in Hilbert spaces. One of the main reasons to equip the classical Cesáro means method with the shrinking projection method is to establish strong convergence results which are often required in infinite-dimensional functional spaces. As a consequence, the convergence analysis is carried out under mild conditions on the underlying shrinking Cesáro means method. We emphasize that the results accounted in this manuscript can be considered as an improvement and generalization of various existing exciting results in this field of study.http://link.springer.com/article/10.1186/s13662-020-02800-zCesáro means methodShrinking projection methodSplit equilibrium fixed point problemTotal asymptotically nonexpansive mapping |
| spellingShingle | Samy A. Harisa M. A. A. Khan F. Mumtaz Nashat Faried Ahmed Morsy Kottakkaran Sooppy Nisar Abdul Ghaffar Shrinking Cesáro means method for the split equilibrium and fixed point problems in Hilbert spaces Advances in Difference Equations Cesáro means method Shrinking projection method Split equilibrium fixed point problem Total asymptotically nonexpansive mapping |
| title | Shrinking Cesáro means method for the split equilibrium and fixed point problems in Hilbert spaces |
| title_full | Shrinking Cesáro means method for the split equilibrium and fixed point problems in Hilbert spaces |
| title_fullStr | Shrinking Cesáro means method for the split equilibrium and fixed point problems in Hilbert spaces |
| title_full_unstemmed | Shrinking Cesáro means method for the split equilibrium and fixed point problems in Hilbert spaces |
| title_short | Shrinking Cesáro means method for the split equilibrium and fixed point problems in Hilbert spaces |
| title_sort | shrinking cesaro means method for the split equilibrium and fixed point problems in hilbert spaces |
| topic | Cesáro means method Shrinking projection method Split equilibrium fixed point problem Total asymptotically nonexpansive mapping |
| url | http://link.springer.com/article/10.1186/s13662-020-02800-z |
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