New results on interpolative metric spaces and applications

This paper aims to present novel fixed point results within the framework of interpolative metric spaces, which extend the concept of standard metric spaces. By leveraging the interpolative metriz-ability technique, which preserves completeness, we observe generalized contractions, including Banach contraction, Kannan contraction, and Chatterjea contraction. Additionally, we provide two applications to demonstrate the significance of our contributions to nonlinear analysis, particularly regarding solutions to nonlinear integral and fractional differential equations.