Condensing Operators in Busemann Convex Metric Spaces With Applications to Hammerstein Integral Equations

In this article, we introduce a new class of cyclic and noncyclic condensing operators that extend the notion of condensing mappings previously proposed by Gabeleh and Markin (M. Gabeleh and J. Markin, Optimum solutions for a system of differential equations via measure of noncompactness, Indagationes Mathematicae, 29(3) [2018], 895–906). Within the framework of reflexive Busemann convex spaces, we establish the existence of best proximity points (or pairs) and coupled best proximity points for these operators. To demonstrate the effectiveness of our theoretical findings, we provide several numerical examples. Furthermore, we apply our results to derive the existence of optimum solutions for a system of Hammerstein integral equations, supported by an illustrative numerical example from the application domain.