Abstract
In this paper, we propose a new modified proximal point algorithm for finding a common element of the set of common minimizers of a finite family of convex and lower semi-continuous functions and the set of common fixed points of a finite family of nonexpansive mappings in complete CAT(0) spaces, and prove some convergence theorems of the proposed algorithm under suitable conditions. A numerical example is presented to illustrate the proposed method and convergence result. Our results improve and extend the corresponding results existing in the literature.
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The authors would like to thank the referees for valuable suggestions on the research paper. This paper was supported by the Thailand Research Fund under the project RTA5780007.
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Lerkchaiyaphum, K., Phuengrattana, W. Iterative approaches to solving convex minimization problems and fixed point problems in complete CAT(0) spaces. Numer Algor 77, 727–740 (2018). https://doi.org/10.1007/s11075-017-0337-6
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DOI: https://doi.org/10.1007/s11075-017-0337-6