Cyclic pairs and common best proximity points in uniformly convex Banach spaces
In this article, we survey the existence, uniqueness and convergence of a common best proximity point for a cyclic pair of mappings, which is equivalent to study of a solution for a nonlinear programming problem in the setting of uniformly convex Banach spaces. Finally, we provide an extension of Ed...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2017-06-01
|
| Series: | Open Mathematics |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/math-2017-0059 |
| id |
doaj-5424f9bb22c445de8a8a282a3b838da9 |
|---|---|
| record_format |
Article |
| spelling |
doaj-5424f9bb22c445de8a8a282a3b838da92021-09-06T19:20:09ZengDe GruyterOpen Mathematics2391-54552017-06-0115171172310.1515/math-2017-0059math-2017-0059Cyclic pairs and common best proximity points in uniformly convex Banach spacesGabeleh Moosa0Julia Mary P.1Eldred Eldred A.Anthony2Olela Otafudu Olivier3Department of Mathematics, Ayatollah Boroujerdi University, Boroujerd, IranPG and Research Department of Mathematics, St.Joseph’s college, Trichy, IndiaPG and Research Department of Mathematics, St.Joseph’s college, Trichy, IndiaSchool of Mathematical Sciences, North-West University (Mafikeng campus) Mmabatho 2735, South AfricaIn this article, we survey the existence, uniqueness and convergence of a common best proximity point for a cyclic pair of mappings, which is equivalent to study of a solution for a nonlinear programming problem in the setting of uniformly convex Banach spaces. Finally, we provide an extension of Edelstein’s fixed point theorem in strictly convex Banach spaces. Examples are given to illustrate our main conclusions.https://doi.org/10.1515/math-2017-005990c4847h0946b20common best proximity pointbest proximity paircyclic contractionuniformly convex banach space |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Gabeleh Moosa Julia Mary P. Eldred Eldred A.Anthony Olela Otafudu Olivier |
| spellingShingle |
Gabeleh Moosa Julia Mary P. Eldred Eldred A.Anthony Olela Otafudu Olivier Cyclic pairs and common best proximity points in uniformly convex Banach spaces Open Mathematics 90c48 47h09 46b20 common best proximity point best proximity pair cyclic contraction uniformly convex banach space |
| author_facet |
Gabeleh Moosa Julia Mary P. Eldred Eldred A.Anthony Olela Otafudu Olivier |
| author_sort |
Gabeleh Moosa |
| title |
Cyclic pairs and common best proximity points in uniformly convex Banach spaces |
| title_short |
Cyclic pairs and common best proximity points in uniformly convex Banach spaces |
| title_full |
Cyclic pairs and common best proximity points in uniformly convex Banach spaces |
| title_fullStr |
Cyclic pairs and common best proximity points in uniformly convex Banach spaces |
| title_full_unstemmed |
Cyclic pairs and common best proximity points in uniformly convex Banach spaces |
| title_sort |
cyclic pairs and common best proximity points in uniformly convex banach spaces |
| publisher |
De Gruyter |
| series |
Open Mathematics |
| issn |
2391-5455 |
| publishDate |
2017-06-01 |
| description |
In this article, we survey the existence, uniqueness and convergence of a common best proximity point for a cyclic pair of mappings, which is equivalent to study of a solution for a nonlinear programming problem in the setting of uniformly convex Banach spaces. Finally, we provide an extension of Edelstein’s fixed point theorem in strictly convex Banach spaces. Examples are given to illustrate our main conclusions. |
| topic |
90c48 47h09 46b20 common best proximity point best proximity pair cyclic contraction uniformly convex banach space |
| url |
https://doi.org/10.1515/math-2017-0059 |
| work_keys_str_mv |
AT gabelehmoosa cyclicpairsandcommonbestproximitypointsinuniformlyconvexbanachspaces AT juliamaryp cyclicpairsandcommonbestproximitypointsinuniformlyconvexbanachspaces AT eldredeldredaanthony cyclicpairsandcommonbestproximitypointsinuniformlyconvexbanachspaces AT olelaotafuduolivier cyclicpairsandcommonbestproximitypointsinuniformlyconvexbanachspaces |
| _version_ |
1717777209243992064 |