Approximating Fixed Points of Operators Satisfying (RCSC) Condition in Banach Spaces. (22nd September 2020)

• Record Type: Journal Article
• Authors: Abdeljawad, Thabet; Ullah, Kifayat; Ahmad, Junaid; de la Sen, Manuel; Khan, Junaid
• Other Names: Ru Yuanfang Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2020(2020)
• Publication Date: 2020-09-22
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2020/9851063
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : Let K be a nonempty subset of a Banach space E . A mapping T : K → K is said to satisfy (RCSC) condition if each a, b ∈ K, 1 / 2 a − F a ≤ a − b ⇒ F a − F b ≤ 1 / 3 a − b + a − F b + b − F a . In this paper, we study, under some appropriate conditions, weak and strong convergence for this class of maps through M iterates in uniformly convex Banach space. We also present a new example of mappings with condition (RCSC). We connect M iteration and other well-known processes with this example to show the numerical efficiency of our results. The presented results improve and extend the corresponding results of the literature.