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

被引：3

作者：

Abdeljawad, Thabet ^{[1
,2
]}

Ullah, Kifayat ^{[3
]}

Ahmad, Junaid ^{[4
]}

Arshad, Muhammad ^{[4
]}

Ma, Zhenhua ^{[5
]}

机构：

[1] Prince Sultan Univ, Dept Math & Sci, POB 66833, Riyadh 11586, Saudi Arabia

[2] China Med Univ, Dept Med Res, Taichung 40402, Taiwan

[3] Univ Lakki Marwat, Dept Math Sci, Lakki Marwat 28420, Khyber Pakhtunk, Pakistan

[4] Int Islamic Univ, Dept Math & Stat, Islamabad 44000, Pakistan

[5] Hebei Univ Architecture, Dept Math & Phys, Zhangjiakou 075024, Peoples R China

来源：

AIMS MATHEMATICS | 2022年 / 7卷 / 11期

关键词：

Banach space; enriched mapping; K; -iteration; condition (I); rate of convergence; APPROXIMATING FIXED-POINTS; PROPERTY; THEOREM; WEAK;

D O I：

10.3934/math.20221108

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：20247 / 20258

页数：12

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