A new approach for fixed point theorems for C-class functions in Hilbert C^∗-modules

In this paper, we introduced a new contraction principle via altering distance and C-class functions with rational forms which extends and generalizes the existing version provided by Hasan Ranjbar et al. [H. Ranjbar, A. Niknam, A fixed point theorem in Hilbert C^∗-modules, Korean J. Math., 30 (2022), 297–304]. Specifically, the rational forms involved in the contraction condition we presented involve the p-th power of the displacements which can exceed the second power mentioned in Hasan Ranjbar et al.’s paper. Moreover, we also proved a fixed point theorem for this type of contraction in the Hilbert C^∗-module. Some adequate examples were provided to support our results. As an application, we applied our result to prove the existence of a unique solution to an integral equation and a second-order (p, q)-difference equation with integral boundary value conditions.