On best proximity points in b-multiplicative metric spaces using R-functions with an application

In this paper, we introduce some rational cyclic conditions in b-multiplicative metric spaces. These conditions generalize existing rational cyclic conditions studied in standard metric frameworks. We establish several best proximity point theorems for a pair of mappings that satisfy these conditions in b-multiplicative metric spaces, thereby broadening the scope of fixed point and best proximity point theory. To illustrate the theoretical results, we provide an application to a nonlinear integral equation.