Two new iterative schemes to approximate the fixed points for mappings
Author:
Deshmukh Aniruddha1, Gopal Dhananjay2, Rakocević Vladimir3
Affiliation:
1. Department of Mathematics , Indian Institute of Technology , Indore 452020 , India 2. Department of Mathematics Guru Ghasidas Vishwavidyalaya , Bilaspur Chhattisgarh 495009 , India 3. Faculty of Sciences and Mathematics , University of Niš , Višegradska 33, 18000 Niš , Serbia
Abstract
Abstract
In this article, we present a study of two iterative schemes to approximate the fixed points of enriched non-expansive maps and enriched generalized non-expansive maps. The schemes introduced in this article generalize those given by Thakur et al. in (“A new iterative scheme for approximating fixed points of nonexpansive mappings,” Filomat, vol. 30, no. 10, pp. 2711–2720, 2016.) and Ali et al. in (“Approximation of Fixed points for Suzuki’s generalized nonexpansive mappings,” Mathematics, vol. 7, no. 6, pp. 522–532, 2019.) in a sense that our schemes work for larger classes of enriched mappings and the schemes given by Thakur et al. and Ali et al. reduce to a particular case of our iterative techniques. Taking inspiration from Berinde (“Picard iteration converges faster than Mann iteration for a class of quasi-contractive operators,” Fixed Point Theory Appl., vol. 2004, no. 2, pp. 97–105, 2004.) and Maniu (“On a three-step iteration process for Suzuki mappings with qualitative study,” Numer. Funct. Anal. Optim., 2020.), we also give stability results of the our procedures for enriched contractions (introduced by Berinde in 2019). Lastly, we compare the rate of convergence of our schemes with each other and the conventional Krasnoselskii iteration process used for approximating fixed points of enriched contractions along with some examples. As an application to the proposed iterative schemes, we give a few results on the solutions of linear system of equations.
Publisher
Walter de Gruyter GmbH
Subject
Applied Mathematics,General Physics and Astronomy,Mechanics of Materials,Engineering (miscellaneous),Modeling and Simulation,Computational Mechanics,Statistical and Nonlinear Physics
Reference38 articles.
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