Best Proximity Point Results for Modified α - ψ -Proximal Rational Contractions

Abstract

We first introduce certain new concepts of $\alpha$-$\eta$-proximal admissible and $\alpha$-$\eta$-$\psi$-rational proximal contractions of the first and second kinds. Then we establish certain best proximity point theorems for such rational proximal contractions in metric spaces. As an application, we deduce best proximity and fixed point results in partially ordered metric spaces. The presented results generalize and improve various known results from best proximity point theory. Several interesting consequences of our obtained results are presented in the form of new fixed point theorems which contain famous Banach's contraction principle and some of its generalizations as special cases. Moreover, some examples are given to illustrate the usability of the obtained results.