• Korean Journal of Mathematics
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• v.31 no.3
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• pp.373-383
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• 2023

The aim of this paper is to prove some new approximate best proximity pair theorems on metric spaces using contraction mappings such as P-Bianchini contraction, P - B contraction and so on. A few examples are provided to exemplify our findings. Finally, we discuss some applications that are related to the main results.

• Nonlinear Functional Analysis and Applications
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• v.29 no.2
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• pp.581-596
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• 2024

A new variety of non-self generalized proximal contraction, called Hardy-Rogers α⁺F-proximal contraction, is shown in this work. Also, with an example, we prove that such contractions satisfying some conditions must have a unique best proximity point. For some particular values of the constants, that we have used to generalize the proximal contraction, we conclude different α⁺F-proximal contraction results of the types Ćirić, Chatterjea, Reich, Kannan, and Banach with proof, that all such type of contractions must have unique best proximity point. We also apply our result to solve a functional equation.