The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
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EXISTENCE OF SELECTION MAP AND THE RELATED FIXED POINT RESULTS ON HYPERCONVEX PRODUCT SPACES

  • A. Herminau Jothy (Department of Mathematics, Bharathidasan University) ;
  • P. S. Srinivasan (Department of Mathematics, Bharathidasan University) ;
  • R. Theivaraman (Department of Mathematics, Bharathidasan University)
  • Received : 2023.11.28
  • Accepted : 2024.06.26
  • Published : 2024.08.31
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Abstract

The main aim of this article is to present new fixed point results concerning existence of selection for a multivalued map on hyperconvex product space taking values on bounded, externally hyperconvex subsets under some appropriate hypothesis. Our results are significant extensions of some pioneering results in the literature, in particular M. A. Khamsi, W. A. Krik and Carlos Martinez Yanez, have proved the existence of single valued selection of a lipschitzian multi-valued map on hyperconvex space. Some suitable examples are also given to support and understand the applicability of our results.

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References

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