Interpolative Contractions for $b$-metric Spaces and Their Applications
DOI:
https://doi.org/10.29020/nybg.ejpam.v18i3.6113Keywords:
Common fixed points; $b$-metric space; integral equation; functional equation.Abstract
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. Karap\i 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.
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Copyright (c) 2025 Dasari Ratna Babu, Naga Koteswara Rao Koduru
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