Generalized enriched cyclic contractions with application to generalized iterated function system. (January 2022)

• Record Type: Journal Article
• Authors: Abbas, Mujahid; Anjum, Rizwan; Iqbal, Hira
• Is Part Of: Chaos, solitons and fractals. Volume 154(2022)
• Publication Date: 2022-01
• Subjects: Fixed point -- Cyclic contraction -- Fractal -- Iterated function system; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2021.111591
• Languages: English
• ISSNs: 0960-0779

Abstract

Highlights: The purpose of this article is to initiate a new type of cyclic contraction mapping and establish a fixed point theorem in Banach space. To approximate the fixed point of such a mapping, a convergence theorem for the Krasnoselskij iteration is presented for which a priori and a posterior error estimates are also determined. As an application, we investigate the iterated function systems (IFS) comprised of generalized cyclic contraction mappings. Some examples are also presented to validate the results. Abstract: The purpose of this article is to initiate a new class of cyclic contraction mappings and establish a related fixed point theorem in the framework of a Banach space. To approximate the fixed point, a convergence theorem employing the Krasnoselskij iteration is presented for which a priori and a posterior error estimates are also determined. These results modify and extend several comparable results in the existing literature. As an application, we investigate the iterated function system (IFS) comprised of generalized cyclic contraction mappings. Some examples are also presented to validate the results.