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Proximal point algorithms based on S-iterative technique for nearly asymptotically quasi-nonexpansive mappings and applications

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Abstract

In this paper, we combine the S-iteration process introduced by Agarwal et al. (J. Nonlinear Convex Anal., 8(1), 61–79 2007) with the proximal point algorithm introduced by Rockafellar (SIAM J. Control Optim., 14, 877–898 1976) to propose a new modified proximal point algorithm based on the S-type iteration process for approximating a common element of the set of solutions of convex minimization problems and the set of fixed points of nearly asymptotically quasi-nonexpansive mappings in the framework of CAT(0) spaces and prove the △-convergence of the proposed algorithm for solving common minimization problem and common fixed point problem. Our result generalizes, extends and unifies the corresponding results of Dhompongsa and Panyanak (Comput. Math. Appl., 56, 2572–2579 2008), Khan and Abbas (Comput. Math. Appl., 61, 109–116 2011), Abbas et al. (Math. Comput. Modelling, 55, 1418–1427 2012) and many more.

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Acknowledgments

The authors would like to thank the editor and referees for useful comments and suggestions.

Funding

The second author is supported by the Council of Scientific and Industrial Research (CSIR), New Delhi, India, through grant 09/013(0584)/2015-EMR-I.

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Authors and Affiliations

  1. Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi, 221005, India

    D. R. Sahu & Ajeet Kumar

  2. Department of Mathematics, Gyeongsang National University, Jinju, 52828, Korea

    Shin Min Kang

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

    Shin Min Kang

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  1. D. R. Sahu
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Correspondence to Shin Min Kang.

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Sahu, D.R., Kumar, A. & Kang, S.M. Proximal point algorithms based on S-iterative technique for nearly asymptotically quasi-nonexpansive mappings and applications. Numer Algor 86, 1561–1590 (2021). https://doi.org/10.1007/s11075-020-00945-2

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