1. Fixed points of Mizoguchi–Takahashi contraction on a metric space with a graph and applications.
- Author
-
Sultana, Asrifa and Vetrivel, V.
- Subjects
- *
FIXED point theory , *CONTRACTION operators , *METRIC spaces , *GRAPH theory , *MATHEMATICAL mappings , *NONLINEAR systems - Abstract
Abstract: In this paper we extend Mizoguchi–Takahashi's fixed point theorem for multi-valued mappings on a metric space endowed with a graph. As an application, we establish a fixed point theorem on an ε-chainable metric space for mappings satisfying Mizoguchi–Takahashi contractive condition uniformly locally. Also, we establish a result on the convergence of successive approximations for certain operators (not necessarily linear) on a Banach space as another application. Consequently, this result yields the Kelisky–Rivlin theorem on iterates of the Bernstein operators on the space and also enables us study the asymptotic behaviour of iterates of some nonlinear Bernstein type operators on . [Copyright &y& Elsevier]
- Published
- 2014
- Full Text
- View/download PDF