R-fonksiyonları yardımıyla bazı en iyi yakınlık noktası sonuçları ve uygulaması üzerine

This thesis explores the intricate domains of best proximity point and fixed point theories, structured into five comprehensive chapters. The first chapter introduces the thesis by outlining its motivation and providing essential background knowledge on the relevant mathematical theories. In the second chapter, we delve into the basic terminology, notations, and theorems that underpin our subsequent findings. Our primary contributions are presented in the third chapter, where we introduce a novel class of functions, including R-functions, and develop a new type of R-contraction. We also redefine the P-property and establish new results for best proximity points and fixed points, supported by an illustrative example to showcase the applicability of our results. The fourth chapter concludes the thesis by summarizing our findings and suggesting directions for future research. This work not only contributes to the existing mathematical literature but also opens new avenues for further theoretical and applied investigations.