@article{Huang2023, 
author = {Hui Huang and Xue Qian},
title = {Common fixed point of nonlinear contractive mappings},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {1},
pages = {607-621},
keywords = {common fixed point, nonlinear contraction, nonexpansive mapping, asymptotical regularity, complete metric space},
url = {https://www.sciopen.com/article/10.3934/math.2023028},
doi = {10.3934/math.2023028},
abstract = {The purpose of this paper is to study the existence of a common fixed point for a pair of mappings without assumption of the contractive coefficient being fixed and less than 1. By replacing the fixed contractive coefficient with a nonlinear contractive function, we establish a unique common fixed point theorem for a pair of asymptotically regular self-mappings with either orbital continuity or    q-continuity in a metric space. Moreover, by the asymptotical regularity of two approximate mappings, we prove that a pair of nonexpansive and continuous self-mappings, which are defined on a nonempty closed convex subset of a Banach space, have a common fixed point. Some examples are given to illustrate that our results are extensions of a recent result in the existing literature.}
}