Best proximity points in ultrametric spaces
Karim Chaira, Samih Lazaiz
TL;DR
This paper investigates the existence of best proximity pairs in ultrametric spaces, generalizing known approximation results and establishing new fixed point theorems under certain conditions.
Contribution
It introduces new conditions for the existence of best proximity pairs in ultrametric spaces and extends classical approximation theorems to this setting.
Findings
Existence of best proximity pairs under suitable assumptions
Generalization of classical best approximation results
Derivation of new fixed point theorems
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 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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Taxonomy
TopicsFixed Point Theorems Analysis