Existence and Convergence Theorems For Best Proximity Points of Proximal Multi-Valued Nonexpansive Mappings - Sarnmeta, Panitarn; Suantai, Suthep (Communications in Mathematics and Applications, 2019)
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.
Keywords: Proximal multi-valued nonexpansive; Best proximity point