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An Extension of Set-Valued Contraction Principle for Mappings on a Metric Space with a Graph and Application
Published in Taylor and Francis Inc.
2017
Volume: 38
   
Issue: 8
Pages: 1060 - 1068
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]. © 2017 Taylor & Francis.
About the journal
JournalData powered by TypesetNumerical Functional Analysis and Optimization
PublisherData powered by TypesetTaylor and Francis Inc.
ISSN01630563
Open AccessNo
Concepts (12)
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    Banach spaces
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    FIXED POINT ARITHMETIC
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    Mapping
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    Mathematical operators
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    Set theory
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    Topology
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    BERNSTEIN OPERATOR
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    Fixed points
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    Graph
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    METRIC SPACES
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    SET-VALUED MAPPING
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    Graph theory