Existence and convergence results for a class of non-expansive type mappings in Banach spaces-Reference-Cited by-同舟云学术

Existence and convergence results for a class of non-expansive type mappings in Banach spaces

Published:2023 Issue:4 Volume:37 Page:1187-1206
ISSN:0354-5180
Container-title:Filomat
language:en
Short-container-title:Filomat

Author:

Bera Ashis¹,Chanda Ankush²,Dey Lakshmi³,Garai Hiranmoy⁴,Rakocevic Vladimir⁵

Affiliation:

1. Department of Mathematics, Vellore Institute of Technology Chennai, India

2. Department of Mathematics, Vellore Institute of Technology, Vellore, India

3. Department of Mathematics, National Institute of Technology Durgapur, India

4. Department of Science and Humanities, Siliguri Government Polytechnic, Siliguri, India

5. Department of Mathematics, Faculty of Sciences and Mathematics, University of Niš, Niš, Serbia

Abstract

In this article, we concentrate on common fixed points of a pair of generalized non-expansive mappings, viz., generalized ?-Reich-Suzuki non-expansive mappings. In this sequel, we introduce the three step Abbas-Nazir iterative algorithm for a pair of mappings. Then we obtain some results related to weak and strong convergence of sequences, satisfying this iterative algorithm, to obtain the common fixed points of two generalized ?-Reich-Suzuki non-expansive mappings. Finally, we compare the convergence rate of our iteration technique to that of some well-known iteration techniques by some constructive numerical examples.

Publisher

National Library of Serbia

Subject

General Mathematics

Reference36 articles.

1. M. Aliyari, M. Gabeleh and E. Karapınar. Mann and Ishikawa iterative processes for cyclic relatively nonexpansive mappings in uniformly convex Banach spaces. J. Nonlinear Convex Anal., 22(4):699-713, 2021.

2. M. Abbas and T. Nazir. A new faster iteration process applied to constrained minimization and feasibility problems. Mat. Vesnik, 66(2):223-234, 2014.

3. R.P. Agarwal, D. O’Regan, and D.R. Sahu. Iterative construction of fixed points of nearly asymptotically nonexpansive mappings. J. Nonlinear Convex Anal., 8(1):61-79, 2007.

4. J. Ali and F. Ali. Approximation of common fixed points and the solution of image recovery problem. Results Math., 74(4), 2019. Article No. 130.

5. K. Aoyama and F. Kohsaka. Fixed point theorem for α-nonexpansive mappings in Banach spaces. Nonlinear Anal., 74(13):4387- 4391, 2011.