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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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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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Authors and Affiliations

  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), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok, 10140, Thailand

    Nuttapol Pakkaranang & Poom Kumam

  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), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok, 10140, Thailand

    Poom Kumam

  3. Department of Mathematics Education and the RINS, Gyeongsang National University, Jinju, 660-701, Korea

    Yeol Je Cho

  4. Center for General Education, China Medical University, Taichung, 40402, Taiwan

    Yeol Je Cho

Authors
  1. Nuttapol Pakkaranang
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  2. Poom Kumam
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  3. Yeol Je Cho
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Correspondence to Poom Kumam.

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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

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