Cyclic (noncyclic) phi-condensing operator and its application to a system of differential equations - Moosa Gabeleh, Moosa; Moshokoa, Philemon; Vetro, Calogero (Nonlinear Analysis: Modelling and Control, 2019)
We 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.
Keywords: best proximity pair; noncyclic φ-condensing operator; ordinary differential equations; strictly convex Banach space