Common Best Proximity Points and Completeness of ℱ−Metric Spaces

Abstract

In this paper, we introduce three classes of proximal contractions that are called the proximally λ−ψ−dominated contractions, generalized ηβγ−proximal contractions and Berinde-type weak proximal contractions, and obtain common best proximity points for these proximal contractions in the setting of F−metric spaces. Further, we obtain the best proximity point result for generalized α−φ−proximal contractions in F−metric spaces. As an application, fixed point and coincidence point results for these contractions are obtained. Some examples are provided to support the validity of our main results. Moreover, we obtain a completeness characterization of the F−metric spaces via best proximity points.

Keywords

• common best proximity point
• proximally <i>λ</i>−<i>ψ</i>−dominated contraction
• η β γ − proximal contraction%22%2C%22default_operator%22%3A%22AND%22%7D%7D%7D"> generalized <named-content content-type="inline-formula"><inline-formula> <mml:math id="mm992"> <mml:semantics> <mml:mrow> <mml:msubsup> <mml:mi>η</mml:mi> <mml:mrow> <mml:mi>β</mml:mi> </mml:mrow> <mml:mi>γ</mml:mi> </mml:msubsup> <mml:mo>−</mml:mo> </mml:mrow> </mml:semantics> </mml:math> </inline-formula></named-content>proximal contraction
• Berinde-type weak proximal contraction
• generalized <i>α</i>−<i>φ</i>−proximal contraction
• ℱ−metric spaces