Best proximity points in ultrametric spaces

Published 14 Apr 2021 in math.FA | (2104.06748v1)

Abstract: In the present paper, we study the existence of best proximity pair in ultrametric spaces. We show, under suitable assumptions, that the proximinal pair $(A,B)$ has a best proximity pair. As a consequence we generalize a well known best approximation result and we derive some fixed point theorems. Moreover, we provide examples to illustrate the obtained results.

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