Interpolative Contractions for $b$-metric Spaces and Their Applications (European Journal of Pure and Applied Mathematics, 2025)
In this research, we introduce the interpolative contractions for a pair of maps in $b$-metric spaces and we utilize the idea of interpolation in complete $b$-metric spaces to prove the associated common fixed point theorems. Our findings generalize and expand the findings of Edraoui et al. \cite{Edraoui} and E. Karapı nar \cite{Erdal} from the metric space setting to $b$-metric spaces. We provide instances to support our conclusions. We offer implementations to solve Fredholm-type nonlinear integral equations and functional equations that emerge in dynamic programming in order to illustrate the importance of our theoretical findings.