Proximal point algorithms for solving convex minimization problem and common fixed points problem of asymptotically quasi-nonexpansive mappings in CAT(0) spaces with convergence analysis |
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| Authors: | Nuttapol Pakkaranang Poom Kumam Yeol Je Cho |
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| Affiliation: | 1.KMUTTFixed Point Research Laboratory, Department of Mathematics, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Faculty of Science,King Mongkut’s University of Technology Thonburi (KMUTT),Bangkok,Thailand;2.KMUTT-Fixed Point Theory and Applications Research Group (KMUTT-FPTA), Theoretical and Computational Science Center (TaCS), Science Laboratory Building, Faculty of Science,King Mongkut’s University of Technology Thonburi (KMUTT),Bangkok,Thailand;3.Department of Mathematics Education and the RINS,Gyeongsang National University,Jinju,Korea;4.Center for General Education,China Medical University,Taichung,Taiwan |
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| Abstract: | In this paper, we introduce the modified proximal point algorithm for common fixed points of asymptotically quasi-nonexpansive mappings in CAT(0) spaces and also prove some convergence theorems of the proposed algorithm to a common fixed point of asymptotically quasi-nonexpansive mappings and a minimizer of a convex function. The main results in this paper improve and generalize the corresponding results given by some authors. Moreover, we then give numerical examples to illustrate and show efficiency of the proposed algorithm for supporting our main results. |
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