An Extension of Set-Valued Contraction Principle for Mappings on a Metric Space with a Graph and Application. (3rd August 2017) - Sultana, Asrifa; Vetrivel, V.
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].