On the convergence of an iterative process for enriched Suzuki nonexpansive mappings in Banach spaces

Thabet Abdeljawad; Kifayat Ullah; Junaid Ahmad; Muhammad Arshad; Zhenhua Ma; Thabet Abdeljawad; Kifayat Ullah; Junaid Ahmad; Muhammad Arshad; Zhenhua Ma

doi:10.3934/math.20221108

AIMS Mathematics

2022, Volume 7, Issue 11: 20247-20258. doi: 10.3934/math.20221108

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Research article

On the convergence of an iterative process for enriched Suzuki nonexpansive mappings in Banach spaces

1.
Department of Mathematics and Sciences, Prince Sultan University, P.O. Box 66833, Riyadh 11586, Saudi Arabia
2.
Department of Medical Research, China Medical University, Taichung 40402, Taiwan
3.
Department of Mathematical Sciences, University of Lakki Marwat, Lakki Marwat 28420, Khyber Pakhtunkhwa, Pakistan
4.
Department of Mathematics and Statistic, International Islamic University, Islamabad 44000, Pakistan
5.
Department of Mathematics and Physics, Hebei University of Architecture, Zhangjiakou 075024, China

Received: 29 June 2022 Revised: 25 August 2022 Accepted: 30 August 2022 Published: 16 September 2022
MSC : 47H09, 47H10

We study the existence and approximation of fixed points for the recently introduced class of mappings called enriched Suzuki nonexpansive mappings in the setting of Banach spaces. We use the modified $ K $-iteration process to establish the main results of the paper. The class of enriched Suzuki nonexpansive operators is an important class of nonlinear operators that includes properly the class of Suzuki nonexpansive operators as well as enriched nonexpansive operators. Various assumptions are imposed on the domain or on the operator to establish the main convergence theorems. Eventually, a numerical example of enriched Suzuki nonexpansive operators is used to show the effectiveness of the studied iteration scheme. The main outcome of the paper is new and essentially suggests a new direction for researchers who are working on fixed point problems in a Banach space setting. Our results improve and extend some main results due to Hussain et al. (J. Nonlinear Convex Anal. 2018, 19, 1383–1393.), Ullah et al. (Axioms 2022, 1.) and others.
- Banach space,
- enriched mapping,
- K-iteration,
- condition (I),
- rate of convergence
Citation: Thabet Abdeljawad, Kifayat Ullah, Junaid Ahmad, Muhammad Arshad, Zhenhua Ma. On the convergence of an iterative process for enriched Suzuki nonexpansive mappings in Banach spaces[J]. AIMS Mathematics, 2022, 7(11): 20247-20258. doi: 10.3934/math.20221108

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Abstract

We study the existence and approximation of fixed points for the recently introduced class of mappings called enriched Suzuki nonexpansive mappings in the setting of Banach spaces. We use the modified $ K $-iteration process to establish the main results of the paper. The class of enriched Suzuki nonexpansive operators is an important class of nonlinear operators that includes properly the class of Suzuki nonexpansive operators as well as enriched nonexpansive operators. Various assumptions are imposed on the domain or on the operator to establish the main convergence theorems. Eventually, a numerical example of enriched Suzuki nonexpansive operators is used to show the effectiveness of the studied iteration scheme. The main outcome of the paper is new and essentially suggests a new direction for researchers who are working on fixed point problems in a Banach space setting. Our results improve and extend some main results due to Hussain et al. (J. Nonlinear Convex Anal. 2018, 19, 1383–1393.), Ullah et al. (Axioms 2022, 1.) and others.

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