Remarks on Minimal Sets for Cyclic Mappings in Uniformly Convex Banach Spaces |
| |
Authors: | Moosa Gabeleh |
| |
Institution: | 1. Department of Mathematics, Ayatollah Boroujerdi University, Boroujerd, Iran;2. School of Mathematics, Institute for Research in Fundamental Sciences (IPM), Tehran, Irangab.moo@gmail.com Gabeleh@abru.ac.ir |
| |
Abstract: | In this article, we prove that every nonempty and convex pair of subsets of uniformly convex in every direction Banach spaces has the proximal normal structure and then we present a best proximity point theorem for cyclic relatively nonexpansive mappings in such spaces. We also study the structure of minimal sets of cyclic relatively nonexpansive mappings and obtain the existence results of best proximity points for cyclic mappings using some new geometric notions on minimal sets. Finally, we prove a best proximity point theorem for a new class of cyclic contraction-type mappings in the setting of uniformly convex Banach spaces and so, we improve the main conclusions of Eldred and Veeramani. |
| |
Keywords: | Best proximity point cyclic relatively nonexpansive mapping proximal normal structure uniformly convex Banach space |
|
|