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Numerical Algorithms
Published in: Numerical Algorithms 4/2021

12-06-2020 | Original Paper

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

Authors: D. R. Sahu, Ajeet Kumar, Shin Min Kang

Published in: Numerical Algorithms | Issue 4/2021

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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.
previous article Minimum residual modified HSS iteration method for a class of complex symmetric linear systems
next article Continuous and discrete zeroing dynamics models using JMP function array and design formula for solving time-varying Sylvester-transpose matrix inequality

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Metadata
Title
Proximal point algorithms based on S-iterative technique for nearly asymptotically quasi-nonexpansive mappings and applications
Authors
D. R. Sahu
Ajeet Kumar
Shin Min Kang
Publication date
12-06-2020
Publisher
Springer US
Published in
Numerical Algorithms / Issue 4/2021
Print ISSN: 1017-1398
Electronic ISSN: 1572-9265
DOI
https://doi.org/10.1007/s11075-020-00945-2

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