The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
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FIXED POINTS OF SET-VALUED MAPPINGS IN RELATIONAL METRIC SPACES

  • Received : 2020.04.30
  • Accepted : 2021.07.22
  • Published : 2021.08.31
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Abstract

In this paper, we generalize the notion of comparable set-valued mappings by introducing two types of 𝓡-closed set-valued mappings and utilize these to obtain an analogue of celebrated Mizoguchi and Takahashi fixed point theorem in relational metric spaces. To annotate the claims and usefulness of such findings, we prove fixed point results for both set-valued and single-valued mappings and validate the assertions with the help of examples. In this way, these investigations extend, modify and generalize some prominent recent fixed point results obtained by Tiammee and Suantai [24], Amini-Harandi and Emami [4], Prasad and Dimri [19] and several others in the settings of relational metric spaces.

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Acknowledgement

The referees have reviewed the paper very carefully. The authors express their deep thanks for the comments.

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