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Fixed Points of Set Valued Mappings in Terms of Start Point on a Metric Space Endowed with a Directed Graph

Author

Listed:
  • Murchana Neog

    (Department of Mathematics, North Eastern Regional Institute of Science and Technology, Nirjuli 791109, Arunachal Pradesh, India
    These authors contributed equally to this work.)

  • Pradip Debnath

    (Department of Mathematics, North Eastern Regional Institute of Science and Technology, Nirjuli 791109, Arunachal Pradesh, India
    These authors contributed equally to this work.)

Abstract

In the present article, we introduce the new concept of start point in a directed graph and provide the characterizations required for a directed graph to have a start point. We also define the notion of a self path set valued map and establish its relation with start point in the setting of a metric space endowed with a directed graph. Further, some fixed point theorems for set valued maps have been proven in this context. A version of the Knaster–Tarski theorem has also been established using our results.

Suggested Citation

  • Murchana Neog & Pradip Debnath, 2017. "Fixed Points of Set Valued Mappings in Terms of Start Point on a Metric Space Endowed with a Directed Graph," Mathematics, MDPI, vol. 5(2), pages 1-7, April.
    • Handle: RePEc:gam:jmathe:v:5:y:2017:i:2:p:24-:d:96150
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