Convergence of Iterates of α-Bernstein Type Operators via Fixed Point of Generalized JS-Contraction Type Mappings. (23rd May 2022)

• Record Type: Journal Article
• Authors: Mahloul, Nora; Ramoul, Hichem; Abbas, Mujahid
• Is Part Of: Numerical functional analysis and optimization. Volume 43:Number 5(2022)
• Page Start: 580
• Page End: 598
• Publication Date: 2022-05-23
• Subjects: α-Bernstein operators -- Fixed point -- JS-contraction; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2022.2053155
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: The aim of this paper is to establish Kelisky-Rivlin type theorem for α -Bernstein-type operators. To achieve this, we first introduce the concept of a generalized JS-contraction type mapping and then we prove a fixed point theorem which is new and first of its kind in the known literature on fixed point theory. The result presented herein generalizes and improves the main result of Altun et al. [Altun, I., Al Arifi, N., Jleli, M., Lashin, A., Samet, B. (2017). A fixed point theorem for JS-contraction type mappings with applications to polynomial approximations. Filomat . 31(15):4969-4978].