Interpolative Contractions for b-metric Spaces and Their Applications

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. Karap 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.