Best proximity point (pair) theorem using ( α − ς ) Meir-Keeler condensing operators in Busemann convex spaces

Two new class of condensing operators, called ( α − ς ) and ( β − ς ) Meir-Keelercondensing operators, are introduced and used to investigate the existence of best proximity points (pairs) for cyclic (noncyclic) relatively nonexpansive mappings to more general metric space, namely reflexive and Busemann convex space by applying measure of noncompactness. In this way, we extend the main results of the paper [M. Gabeleh, C. Vetro, A new extension of Darbo's fixed point theorem using relatively Meir-Keeler condensing operators, Bull. Aust. Math. Soc., 98 (2022), 247-266] from Banach spaces to Busemann convex metric spaces and by considering appropriate control functions. Some related examples are also presented to describe these classes of operators. Finally, as an application of our main conclusions, we survey the existence of an optimal solution for a certain type of system of integro-differential equations.