Optimal Pair of Fixed Points of Noncyclic Chatterjea-Type Mappings in Busemann Convex Spaces

We introduce and study a new class of noncyclic Chatterjea-type C-nonexpansive mappings in geodesic spaces. We establish a notable existence theorem for best proximity pairs by employing the pivotal geometric property of proximal normal structure within the framework of reflexive Busemann convex spaces. Moreover, we investigate minimal invariant sets associated with these mappings and derive a generalization of the Goebel–Karlovitz lemma. Our main contribution extends this fundamental result to geodesic spaces with property UC, thereby providing a significant generalization of the classical theorem for the case of Chatterjea-type C-nonexpansive mappings.