Best proximity point theorems for proximal multi-valued contractions

Author:

Bunlue Nuttawut1,Cho Yeol2,Suantai Suthep3

Affiliation:

1. Graduate Ph.D. Degree Program in Mathematics, Faculty of Science, Chiang Mai University Chiang Mai, Thailand

2. Department of Mathematics Education, Gyeongsang National University, Jinju , Korea + Center for General Education, China Medical University, Taichung, Taiwan

3. Research Center in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai, Thailand + Data Science Research Center, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai, Thailand

Abstract

In this paper, we introduce new classes of proximal multi-valued contractions in a metric space and proximal multi-valued nonexpansive mappings in a Banach space and show the existence of best proximity points for both classes. Further, for proximal multi-valued nonexpansive mappings, we prove a best proximity point theorem on starshape sets. As a consequence, we also obtain some new fixed point theorems. Finally, we give some examples to illustrate our main results.

Publisher

National Library of Serbia

Subject

General Mathematics

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