Best Proximity Points of Relatively Jaggi Nonexpansive Mappings in Busemann Convex Spaces

Abstract

In this paper, we introduce cyclic (noncyclic) relatively Jaggi nonexpansive mappings on Busemann convex spaces and investigate the existence of their best proximity points (pairs). Furthermore, we extend the notation of relatively u-continuous mappings in geodesic spaces and generalize an existence result of best proximity points from strictly convex Banach spaces to Busemann convex spaces. We also generalize Ky Fan’s best approximation theorem using Schauder’s fixed-point theorem within the framework of Busemann convex spaces. Finally, we examine the existence of common points for a family of relatively u-continuous cyclic compact mappings in Busemann convex spaces, effectively generalizing the Markov–Kakutani theorem. Copyright © 2025 M. Gabeleh et al. Journal of Function Spaces published by John Wiley & Sons Ltd.