Gabeleha, MoosaMoshokoa, Seithuti PhilemonVetro, Calogero2024-11-132024-11-132018-12-021392-5113 (P)2335-8963 (E)http://dx.doi.org/10.15388/NA.2019.6.8https://hdl.handle.net/20.500.14519/1056We establish a best proximity pair theorem for noncyclic ϕ-condensing operators in strictly convex Banach spaces by using a measure of noncompactness. We also obtain a counterpart result for cyclic ϕ-condensing operators in Banach spaces to guarantee the existence of best proximity points, and so, an extension of Darbo’s fixed point theorem will be concluded. As an application of our results, we study the existence of a global optimal solution for a system of ordinary differential equations.985-1000 PagesenAttribution-NonCommercial-ShareAlike 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-sa/4.0/Best proximity pairNoncyclic ϕ-condensing operatorOrdinary differential equationsStrictly convex Banach spaceArticle