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.
@article{bwmeta1.element.doi-10_1515_math-2017-0059,
author = {Moosa Gabeleh and P. Julia Mary and A.Anthony Eldred Eldred and Olivier Olela Otafudu},
title = {Cyclic pairs and common best proximity points in uniformly convex Banach spaces},
journal = {Open Mathematics},
volume = {15},
year = {2017},
pages = {711-723},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_math-2017-0059}
}
Moosa Gabeleh; P. Julia Mary; A.Anthony Eldred Eldred; Olivier Olela Otafudu. Cyclic pairs and common best proximity points in uniformly convex Banach spaces. Open Mathematics, Tome 15 (2017) pp. 711-723. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_math-2017-0059/