  The purpose of this paper is to introduce the class of R-enriched
interpolative Kannan pair and proved a common fixed point result in the context
of R-complete convex metric spaces. Some examples are presented to support the
concepts introduced herein. Moreover, we study the well-posedness, limit
shadowing property and Ulam-Hyers stability of the mappings introduced herein.
Our result extend and generalize several comparable results in the existing
literature.

General Mathematics