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Chantakun, Warinsinee; Yuying, Tadchai; Sattayaporn, Suchinda

Best proximity point and fixed point theorems in complex valued rectangular \(b\)-metric spaces. (English) Zbl 07876128

J. Nonlinear Anal. Optim. 15, No. 1, 13-22 (2024).
Summary: The aim of this paper, by using the concept of continuity of \(\phi:[0, \infty)^2\to[0, \infty)^2\) which satisfies \(\phi(t) \prec t\) and \(\phi(0)=0\) to define some contraction condition of \(T\) introduced by G. Meena [“Best proximity and fixed point results in complex valued rectangular metric spaces”, Glob. J. Pure Appl. Math. 14, No. 5, 689–698 (2018), https://www.ripublication.com/gjpam18/gjpamv14n5_05.pdf)], we prove the unique best proximity point of \(A\) and fixed point of \(T\) in complex valued rectangular \(b\)-metric space. Our results extend and improve the results of [loc. cit.], and many others.

MSC:

47H10 Fixed-point theorems
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47H20 Semigroups of nonlinear operators

Keywords:

best proximity point; rectangular \(b\)-metric spaces; rectangular complex valued \(b\)-metric spaces
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References:

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