New Results on Interpolative Metric Spaces and Applications

Abstract

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 metrizability 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.g solutions to nonlinear integral and fractional differential equations.