We define wt0-distance which is a special type of wt-distance and obtain some best proximity point theorems involving b-simulation functions. Our results are significant, since we replace simulation function with function, metric space b-metric space, w0-distance wt0-distance. also provide examples to support our results.

In this paper, we employ two types of implicit relations to define some new kind proximal contractions and study about their best proximity points. More precisely, use class functions $\mathcal{A}$ $\mathcal{A}'$ explore $\mathcal{A}$, $\mathcal{A}'$-contractions first second type strong $\mathcal{A}'$-contractions. We investigate the existence point results same. It is worth mentioning that we...

We establish some common best proximity point results for generalized α−ψ-proximal contractive non-self mappings. We provide some concrete examples. We also derive some consequences on some best proximity results on a metric space endowed with a graph. 2000 Mathematics Subject Classification: 47H10, 54H25.