@article{Aslantas2024, 
author = {Mustafa Aslantas and Hakan Sahin and Ishak Altun and Taif Hameed SAADOON SAADOON},
title = {A new type of        R  -contraction and its best proximity points},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {4},
pages = {9692-9704},
keywords = {R-contractions, homotopy, best proximity point, fixed point},
url = {https://www.sciopen.com/article/10.3934/math.2024474},
doi = {10.3934/math.2024474},
abstract = {In this paper, we aim to overcome the problem given by Abkar et al. [Abstr. Appl. Anal., 2013 (2013), 189567], and so to obtain real generalizations of fixed point results in the literature. In this direction, we introduce a new class of functions, which include        R  -functions. Thus, we present a new type of        R   -contraction and weaken        R  -contractions that have often been studied recently. We also give a new definition of the    P-property. Hence, we obtain some best proximity point results, including fixed point results for the new kind of        R  -contractions. Then, we provide an example to show the effectiveness of our results. Finally, inspired by a nice and interesting technique, we investigate the existence of a best proximity point of the homotopic mappings with the help of our main result.}
}