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New hybrid algorithms for global minimization of common best proximity points of some generalized nonexpansive mappings

Puangpee Jenwit (Faculty of Science, Chiang Mai University, Chiang Mai, Thailand)
Suantai Suthep (Data Science Research Center, Research Center in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai, Thailand)

In this paper, we introduce two hybrid algorithms for finding a common best proximity point of two best proximally nonexpansive mappings. We establish strong convergence theorems of the proposed algorithms under some control conditions in a real Hilbert space. Moreover, some numerical examples are given for supporting our main theorems.

Keywords: hybrid algorithm, common best proximity point, global minimization problem, best proximally nonexpansive mapping