Relaxed iterative algorithms for a system of generalized mixed equilibrium problems and a countable family of totally quasi-Phi-asymptotically nonexpansive multi-valued maps, with applications
Abstract In this article, a Krasnoselskii-type and a Halpern-type algorithm for approximating a common fixed point of a countable family of totally quasi-ϕ-asymptotically nonexpansive nonself multi-valued maps and a solution of a system of generalized mixed equilibrium problem are constructed. Stron...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2017-11-01
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| Series: | Fixed Point Theory and Applications |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13663-017-0616-x |
| _version_ | 1818981256689352704 |
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| author | CE Chidume OM Romanus UV Nnyaba |
| author_facet | CE Chidume OM Romanus UV Nnyaba |
| author_sort | CE Chidume |
| collection | DOAJ |
| description | Abstract In this article, a Krasnoselskii-type and a Halpern-type algorithm for approximating a common fixed point of a countable family of totally quasi-ϕ-asymptotically nonexpansive nonself multi-valued maps and a solution of a system of generalized mixed equilibrium problem are constructed. Strong convergence of the sequences generated by these algorithms is proved in uniformly smooth and strictly convex real Banach spaces with the Kadec-Klee property. Several applications of our theorems are also presented. Finally, our theorems are a significant improvement of several important recent results. |
| first_indexed | 2024-12-20T17:28:26Z |
| format | Article |
| id | doaj.art-04768c8fe93441a9acc0e6c49c20abb6 |
| institution | Directory Open Access Journal |
| issn | 1687-1812 |
| language | English |
| last_indexed | 2024-12-20T17:28:26Z |
| publishDate | 2017-11-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Fixed Point Theory and Applications |
| spelling | doaj.art-04768c8fe93441a9acc0e6c49c20abb62022-12-21T19:31:27ZengSpringerOpenFixed Point Theory and Applications1687-18122017-11-012017111510.1186/s13663-017-0616-xRelaxed iterative algorithms for a system of generalized mixed equilibrium problems and a countable family of totally quasi-Phi-asymptotically nonexpansive multi-valued maps, with applicationsCE Chidume0OM Romanus1UV Nnyaba2African University of Science and TechnologyAfrican University of Science and TechnologyAfrican University of Science and TechnologyAbstract In this article, a Krasnoselskii-type and a Halpern-type algorithm for approximating a common fixed point of a countable family of totally quasi-ϕ-asymptotically nonexpansive nonself multi-valued maps and a solution of a system of generalized mixed equilibrium problem are constructed. Strong convergence of the sequences generated by these algorithms is proved in uniformly smooth and strictly convex real Banach spaces with the Kadec-Klee property. Several applications of our theorems are also presented. Finally, our theorems are a significant improvement of several important recent results.http://link.springer.com/article/10.1186/s13663-017-0616-xgeneralized mixed equilibrium problemstotally quasi-ϕ-asymptotically nonexpansive nonself multi-valued mapsstrong convergenceequally continuous maps |
| spellingShingle | CE Chidume OM Romanus UV Nnyaba Relaxed iterative algorithms for a system of generalized mixed equilibrium problems and a countable family of totally quasi-Phi-asymptotically nonexpansive multi-valued maps, with applications Fixed Point Theory and Applications generalized mixed equilibrium problems totally quasi-ϕ-asymptotically nonexpansive nonself multi-valued maps strong convergence equally continuous maps |
| title | Relaxed iterative algorithms for a system of generalized mixed equilibrium problems and a countable family of totally quasi-Phi-asymptotically nonexpansive multi-valued maps, with applications |
| title_full | Relaxed iterative algorithms for a system of generalized mixed equilibrium problems and a countable family of totally quasi-Phi-asymptotically nonexpansive multi-valued maps, with applications |
| title_fullStr | Relaxed iterative algorithms for a system of generalized mixed equilibrium problems and a countable family of totally quasi-Phi-asymptotically nonexpansive multi-valued maps, with applications |
| title_full_unstemmed | Relaxed iterative algorithms for a system of generalized mixed equilibrium problems and a countable family of totally quasi-Phi-asymptotically nonexpansive multi-valued maps, with applications |
| title_short | Relaxed iterative algorithms for a system of generalized mixed equilibrium problems and a countable family of totally quasi-Phi-asymptotically nonexpansive multi-valued maps, with applications |
| title_sort | relaxed iterative algorithms for a system of generalized mixed equilibrium problems and a countable family of totally quasi phi asymptotically nonexpansive multi valued maps with applications |
| topic | generalized mixed equilibrium problems totally quasi-ϕ-asymptotically nonexpansive nonself multi-valued maps strong convergence equally continuous maps |
| url | http://link.springer.com/article/10.1186/s13663-017-0616-x |
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