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


  • 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




Proximal multi-valued nonexpansive, Best proximity point


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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How to Cite

Sarnmeta, P., & Suantai, S. (2019). Existence and Convergence Theorems For Best Proximity Points of Proximal Multi-Valued Nonexpansive Mappings. Communications in Mathematics and Applications, 10(3), 369–377. https://doi.org/10.26713/cma.v10i3.1199



Research Article