(untitled) (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. Edraoui and E. Karapı nar 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.