MMN-3674
A new approach to homotopy theory via best proximity point
Hakan Sahin;Abstract
In this paper, we extend the result of Romaguera [20] with the aid of best proximity point theory on partial metric spaces by considering the approach of Haghi et al. [8], and so celebrated Boyd-Wong fixed point theorem [7]. We first introduce two concepts called generalized proximal $BW$-contraction and generalized best $BW$-contraction. Then, we obtain some best proximity point theorems for such mappings. To illustrate the effectiveness of our results, we provide some nontrivial and interesting examples. Finally, unlike homotopy applications existing in the literature, we present for the first time an application of the best proximity result to the homotopy theory.
Vol. 24 (2023), No. 1, pp. 411-428