In 2024, Păcurar and Popescu Fixed point theorem for generalized Chatterjea type mappings, Acta Math. Hungar., 173(2), 2024, 500-509 proved a three-point analog of Chatterjea’s fixed-point theorem. In this paper, we prove various characteristics of generalized Chatterjea type mappings and their connections with generalized Kannan type mappings, Chatterjea type mappings, and mappings contracting perimeters of triangles, in addition to showing that these mappings are continuous at the fixed point.We also derive two fixed point theorems for generalized Chatterjea type mappings in metric spaces by dropping the requirement of completeness in the space involved. Finally, as an application, we investigate the existence of solutions to fractional differential equations with boundary conditions for generalized Chatterjea type mappings.
Bisht et al. (Fri,) studied this question.