Best proximity of proximal $\mathcal{F}^*$-weak contraction

Subject Areas : Fixed point theory

M. Salamatbakhsh ¹ , R. H. Haghi ² , K. Fallahi ³

1 - Department of Mathematics, Payame Noor University, Tehran, Iran
2 - Department of Mathematics, Payame Noor University, Tehran, Iran
3 - Department of Mathematics, Payame Noor University, Tehran, Iran

Received: 2022-01-14 Accepted : 2022-03-04 Published : 2022-03-05

Keywords: Best Proximity point‎, ‎approximatively compact‎, ‎cyclically Cauchy sequence‎, ‎uniform approximation‎, ‎quasi-continuous, ‎proximal $mathcal{F}^{*}$-weak‎ ‎contraction‎, $mathcal{S}$-approximation‎,

Abstract :

‎Best proximity point‎ ‎theorems for self-mappings were investigated with different‎ ‎conditions on spaces for contraction mappings‎. ‎In this‎ ‎paper‎, ‎we prove best proximity point theorems for proximal $\mathcal{F}^{*}$-weak contraction mappings‎.

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