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

Abstract

<abstract><p>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. (<italic>J. Nonlinear Convex Anal.</italic> 2018, <italic>19</italic>, 1383–1393.), Ullah et al. (<italic>Axioms</italic> 2022, 1.) and others.</p></abstract>