An Extension of Set-Valued Contraction Principle for Mappings on a Metric Space with a Graph and Application. (3rd August 2017)

• Record Type: Journal Article
• Authors: Sultana, Asrifa; Vetrivel, V.
• Is Part Of: Numerical functional analysis and optimization. Volume 38:Number 8(2017)
• Page Start: 1060
• Page End: 1068
• Publication Date: 2017-08-03
• Subjects: Bernstein operators -- fixed Point -- graph -- metric space -- set-valued mapping; 47H04 -- 47H10 -- 54H25; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2017.1311346
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: In this paper, we obtain an existence theorem for fixed points of contractive set-valued mappings on a metric space endowed with a graph. This theorem unifies and extends several fixed point theorems for mappings on metric spaces and for mappings on metric spaces endowed with a graph. As an application, we obtain a theorem on the convergence of successive approximations for some linear operators on an arbitrary Banach space. This result yields the well-known Kelisky–Rivlin theorem on iterates of the Bernstein operators on C [0, 1].