Cyclic (noncyclic) phi-condensing operator and its application to a system of differential equations
Articles
Moosa Moosa Gabeleh
Ayatollah Boroujerdi University
Philemon Moshokoa
Tshwane University of Technology
Calogero Vetro
University of Palermo
Published 2019-11-07
https://doi.org/10.15388/NA.2019.6.8
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Keywords

best proximity pair
noncyclic φ-condensing operator
ordinary differential equations
strictly convex Banach space

How to Cite

Moosa Gabeleh M., Moshokoa P. and Vetro C. (2019) “Cyclic (noncyclic) phi-condensing operator and its application to a system of differential equations”, Nonlinear Analysis: Modelling and Control, 24(6), pp. 985–1000. doi: 10.15388/NA.2019.6.8.

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.

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