Best approximation theorems via relatively u -continuous and Jaggi nonexpansive mappings
Moosa Gabeleh, R. Gholipour, Hamid Mazaheri, Seithuti Philemon Moshokoa · Quaestiones Mathematicae · 2024
In this paper, we introduced a new type of cyclic (noncyclic) mappings, called Jaggi relatively nonexpansive mappings and use to investigate the existence of best proximity points (pairs) in the framework of reflexive (strictly convex) Banach spaces by using a geometric concept of proximal normal structure. We also present a best proximity version of Schauder’s fixed point problem for non-self mappings. Finally, we prove the existence of a common best proximity point for an arbitrary family of cyclic relatively u-continuous mappings which are compact and then we obtain a generalization of Markov-Kakutani’s theorem.