@article{Zhou2024, 
author = {Mi Zhou and Arsalan Hojjat Ansari and Choonkil Park and Snježana Maksimović and Zoran D. Mitrović},
title = {A new approach for fixed point theorems for  C-class functions in Hilbert  C∗-modules},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {10},
pages = {28850-28869},
keywords = {fixed point, Hilbert C∗-modules, C-class function},
url = {https://www.sciopen.com/article/10.3934/math.20241400},
doi = {10.3934/math.20241400},
abstract = {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.}
}