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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Acknowledgments
The first author would like to thank the Research Professional Development Project Under the Science Achievement Scholarship of Thailand (SAST) for financial support. Furthermore, then project was supported by the Theoretical and Computation Science (TaCS) Center under Computational and Applied Science for Smart Innovation Cluster (CLASSIC), Faculty of Science, KMUTT. Moreover, Poom Kumam was supported by the Thailand Research Fund (TRF) and the King Mongkut’s University of Technology Thonburi (KMUTT) under the TRF Research Scholar Award (Grant No. RSA6080047).
Yeol Je Cho was supported by Basic Science Research Program through the National Research Foundation funded by the Ministry of Science, ICT and Future Planning (2014RIA2AA01002100).
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Pakkaranang, N., Kumam, P. & Cho, Y.J. 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. Numer Algor 78, 827–845 (2018). https://doi.org/10.1007/s11075-017-0402-1
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DOI: https://doi.org/10.1007/s11075-017-0402-1
Keywords
- Proximal point algorithm
- Convex minimization problem
- Common fixed point
- Asymptotically quasi-nonexpansive mapping
- CAT(0) spaces