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An Extension of Set-Valued Contraction Principle for Mappings on a Metric Space with a Graph and ApplicationPublished in Taylor and Francis Inc.

2017

Volume: 38

Issue: 8

Pages: 1060 - 1068

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]. © 2017 Taylor & Francis.

Topics: Injective metric space (67)%67% related to the paper, Convex metric space (66)%66% related to the paper, Metric differential (66)%66% related to the paper, Closed graph theorem (66)%66% related to the paper and Fixed-point theorem (65)%65% related to the paper

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About the journal

Journal | Data powered by TypesetNumerical Functional Analysis and Optimization |
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Publisher | Data powered by TypesetTaylor and Francis Inc. |

ISSN | 01630563 |

Open Access | No |

Concepts (12)

- Banach spaces
- FIXED POINT ARITHMETIC
- Mapping
- Mathematical operators
- Set theory
- Topology
- BERNSTEIN OPERATOR
- Fixed points
- Graph
- METRIC SPACES
- SET-VALUED MAPPING
- Graph theory