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.

Gabeleh M., Moshokoa S.P., Vetro C. (2019). Cyclic (Noncyclic) ϕ-condensing operator and its application to a system of differential equations. NONLINEAR ANALYSIS, 24(6), 985-1000 [10.15388/NA.2019.6.8].

Cyclic (Noncyclic) ϕ-condensing operator and its application to a system of differential equations

Vetro C.
2019-01-01

Abstract

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.
Settore MAT/05 - Analisi Matematica
https://www.journals.vu.lt/nonlinear-analysis/article/download/14847/13865
Gabeleh M., Moshokoa S.P., Vetro C. (2019). Cyclic (Noncyclic) ϕ-condensing operator and its application to a system of differential equations. NONLINEAR ANALYSIS, 24(6), 985-1000 [10.15388/NA.2019.6.8].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/398450
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