Existence and Convergence Theorems For Best Proximity Points of Proximal Multi-Valued Nonexpansive Mappings

Panitarn Sarnmeta; Suthep Suantai

doi:10.26713/cma.v10i3.1199

Authors

Panitarn Sarnmeta Ph.D. Degree Program in Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai, 50200,
Suthep Suantai Center of Excellence in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200

DOI:

https://doi.org/10.26713/cma.v10i3.1199

Keywords:

Proximal multi-valued nonexpansive, Best proximity point

Abstract

The concepts of proximal contraction and proximal nonexpansive mapping have been investigated and extended in many direction. However, most of these works concern only single-valued mappings. So, in this paper, we introduce a concept of proximal nonexpansive for non-self set-valued mappings and prove the existence of best proximity point for such mappings under appropriate conditions. We also provide an algorithm to approximate a best proximity point of such mappings, and prove its convergence theorem. Moreover, a numerical example supporting our main results is also given.

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