A new modified block iterative algorithm for uniformly quasi-<it>ϕ</it>-asymptotically nonexpansive mappings and a system of generalized mixed equilibrium problems
<p>Abstract</p> <p>In this paper, we introduce a new modified block iterative algorithm for finding a common element of the set of common fixed points of an infinite family of closed and uniformly quasi-<it>ϕ</it>-asymptotically nonexpansive mappings, the set o...
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | article |
| Lenguaje: | EN |
| Publicado: |
SpringerOpen
2011
|
| Materias: | |
| Acceso en línea: | https://doaj.org/article/2414daa7983448169d5dc111651ce044 |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| id |
oai:doaj.org-article:2414daa7983448169d5dc111651ce044 |
|---|---|
| record_format |
dspace |
| spelling |
oai:doaj.org-article:2414daa7983448169d5dc111651ce0442021-12-02T11:31:23ZA new modified block iterative algorithm for uniformly quasi-<it>ϕ</it>-asymptotically nonexpansive mappings and a system of generalized mixed equilibrium problems1687-18201687-1812https://doaj.org/article/2414daa7983448169d5dc111651ce0442011-01-01T00:00:00Zhttp://www.fixedpointtheoryandapplications.com/content/2011/1/35https://doaj.org/toc/1687-1820https://doaj.org/toc/1687-1812<p>Abstract</p> <p>In this paper, we introduce a new modified block iterative algorithm for finding a common element of the set of common fixed points of an infinite family of closed and uniformly quasi-<it>ϕ</it>-asymptotically nonexpansive mappings, the set of the variational inequality for an <it>α</it>-inverse-strongly monotone operator, and the set of solutions of a system of generalized mixed equilibrium problems. We obtain a strong convergence theorem for the sequences generated by this process in a 2-uniformly convex and uniformly smooth Banach space. Our results extend and improve ones from several earlier works.</p> <p> <b>2000 MSC: </b>47H05; 47H09; 47H10.</p> Saewan SiwapornKumam PoomSpringerOpenarticlemodified block iterative algorithminverse-strongly monotone operatorvariational inequalitya system of generalized mixed equilibrium problemuniformly quasi-<it>ϕ</it>-asymptotically nonexpansive mappingApplied mathematics. Quantitative methodsT57-57.97AnalysisQA299.6-433ENFixed Point Theory and Applications, Vol 2011, Iss 1, p 35 (2011) |
| institution |
DOAJ |
| collection |
DOAJ |
| language |
EN |
| topic |
modified block iterative algorithm inverse-strongly monotone operator variational inequality a system of generalized mixed equilibrium problem uniformly quasi-<it>ϕ</it>-asymptotically nonexpansive mapping Applied mathematics. Quantitative methods T57-57.97 Analysis QA299.6-433 |
| spellingShingle |
modified block iterative algorithm inverse-strongly monotone operator variational inequality a system of generalized mixed equilibrium problem uniformly quasi-<it>ϕ</it>-asymptotically nonexpansive mapping Applied mathematics. Quantitative methods T57-57.97 Analysis QA299.6-433 Saewan Siwaporn Kumam Poom A new modified block iterative algorithm for uniformly quasi-<it>ϕ</it>-asymptotically nonexpansive mappings and a system of generalized mixed equilibrium problems |
| description |
<p>Abstract</p> <p>In this paper, we introduce a new modified block iterative algorithm for finding a common element of the set of common fixed points of an infinite family of closed and uniformly quasi-<it>ϕ</it>-asymptotically nonexpansive mappings, the set of the variational inequality for an <it>α</it>-inverse-strongly monotone operator, and the set of solutions of a system of generalized mixed equilibrium problems. We obtain a strong convergence theorem for the sequences generated by this process in a 2-uniformly convex and uniformly smooth Banach space. Our results extend and improve ones from several earlier works.</p> <p> <b>2000 MSC: </b>47H05; 47H09; 47H10.</p> |
| format |
article |
| author |
Saewan Siwaporn Kumam Poom |
| author_facet |
Saewan Siwaporn Kumam Poom |
| author_sort |
Saewan Siwaporn |
| title |
A new modified block iterative algorithm for uniformly quasi-<it>ϕ</it>-asymptotically nonexpansive mappings and a system of generalized mixed equilibrium problems |
| title_short |
A new modified block iterative algorithm for uniformly quasi-<it>ϕ</it>-asymptotically nonexpansive mappings and a system of generalized mixed equilibrium problems |
| title_full |
A new modified block iterative algorithm for uniformly quasi-<it>ϕ</it>-asymptotically nonexpansive mappings and a system of generalized mixed equilibrium problems |
| title_fullStr |
A new modified block iterative algorithm for uniformly quasi-<it>ϕ</it>-asymptotically nonexpansive mappings and a system of generalized mixed equilibrium problems |
| title_full_unstemmed |
A new modified block iterative algorithm for uniformly quasi-<it>ϕ</it>-asymptotically nonexpansive mappings and a system of generalized mixed equilibrium problems |
| title_sort |
new modified block iterative algorithm for uniformly quasi-<it>ϕ</it>-asymptotically nonexpansive mappings and a system of generalized mixed equilibrium problems |
| publisher |
SpringerOpen |
| publishDate |
2011 |
| url |
https://doaj.org/article/2414daa7983448169d5dc111651ce044 |
| work_keys_str_mv |
AT saewansiwaporn anewmodifiedblockiterativealgorithmforuniformlyquasiit981itasymptoticallynonexpansivemappingsandasystemofgeneralizedmixedequilibriumproblems AT kumampoom anewmodifiedblockiterativealgorithmforuniformlyquasiit981itasymptoticallynonexpansivemappingsandasystemofgeneralizedmixedequilibriumproblems AT saewansiwaporn newmodifiedblockiterativealgorithmforuniformlyquasiit981itasymptoticallynonexpansivemappingsandasystemofgeneralizedmixedequilibriumproblems AT kumampoom newmodifiedblockiterativealgorithmforuniformlyquasiit981itasymptoticallynonexpansivemappingsandasystemofgeneralizedmixedequilibriumproblems |
| _version_ |
1718395865180143616 |