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

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...

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Bibliographic Details
Published in:Numerical algorithms Vol. 86; no. 4; pp. 1561 - 1590
Main Authors: Sahu, D. R., Kumar, Ajeet, Kang, Shin Min
Format: Journal Article
Language:English
Published: New York Springer US 01.04.2021
Springer Nature B.V
Subjects:
Algebra
Algorithms
Asymptotic properties
Banach spaces
Computer Science
Iterative methods
Numeric Computing
Numerical Analysis
Optimization
Original Paper
Regularization methods
Theory of Computation
iteration process
Fixed point problem
47H10
convergence
Convex minimization problem
Mean nonexpansive mapping
CAT space
47H09
49M05
Proximal point algorithm
Nearly asymptotically quasi-nonexpansive mapping
ISSN:1017-1398, 1572-9265
Online Access:Get full text
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Summary: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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ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-020-00945-2