Generalized Ulam-Hyers Stability, Well-Posedness and Limit Shadowing of a Fixed Point Problem for Chatterjea Contractive Mappings in $M$-Metric Spaces

Pathaithep Kumrod, Wutiphol Sintunavarat, Yeol Je Cho, Yi-bin Xiao

Abstract

The purpose of this paper is to investigate new types of the Ulam-Hyers stability, the well-posedness and the limit shadowing type of the fixed point problem for Chatterjea contractive mappings in the framework of $M$-metric spaces. Some illustrative examples for showing main results in this paper are also given. The main results in this paper are motivated from the results of Pansuwan et al. [A. Pansuwan, W. Sintunavarat, J.Y. Choi, Y.J. Cho, Ulam-Hyers stability, well-posedness and limit shadowing property of the fixed point problems in M-metric spaces, J. Nonlinear Sci, Appl. 9 (2016) 4489-4499].