  In this paper, we introduce a new category of mappings within metric spaces,
specifically focusing on three-point analogs of the well-established Chatterjea
type mappings. We demonstrate that Chatterjea type mappings and their
three-point analogs are different classes of mappings. A fixed point theorem
for generalized Chatterjea type mappings is established. It is shown that these
mappings are continuous at fixed point. Connections between generalized
Chatterjea type mappings, generalized Kannan type mappings, Chatterjea type
mappings, and mappings contracting perimeters of triangles are found.
Additionally, we derive two fixed point theorems for generalized Chatterjea
type mappings in metric spaces, even when completeness is not mandatory.
