Nonlinear Functional Analysis and Applications

Kyungnam University, Department of Mathematics Eduaction (경남대학교 수학교육과)
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BEST APPROXIMATIONS FOR MULTIMAPS ON ABSTRACT CONVEX SPACES

  • Received : 2020.08.27
  • Accepted : 2020.10.06
  • Published : 2021.03.15
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Abstract

In this article we derive some best approximation theorems for multimaps in abstract convex metric spaces. We are based on generalized KKM maps due to Kassay-Kolumbán, Chang-Zhang, and studied by Park, Kim-Park, Park-Lee, and Lee. Our main results are extensions of a recent work of Mitrović-Hussain-Sen-Radenović on G-convex metric spaces to partial KKM metric spaces. We also recall known works related to single-valued maps, and introduce new partial KKM metric spaces which can be applied our new results.

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References

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