Aslantas, MustafaSahin, HakanAltun, IshakSaadoon, Taif Hameed Saadoon2026-02-082026-02-0820242473-6988https://doi.org/10.3934/math.2024474https://hdl.handle.net/20.500.12885/6104In 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.eninfo:eu-repo/semantics/openAccessR-contractionshomotopybest proximity pointfixed pointArticle10.3934/math.20244749496929704WOS:0011813696000052-s2.0-85187426016Q1Q1