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november 2019 A best proximity point approach to existence of solutions for a system of ordinary differential equations
Moosa Gabeleh, Calogero Vetro
Bull. Belg. Math. Soc. Simon Stevin 26(4): 493-503 (november 2019). DOI: 10.36045/bbms/1576206350

Abstract

We establish the existence of a solution for the following system of differential equations \begin{equation*} \label{system}\begin{cases}x'(t) = f (t, x(t)), & x(t_0) = x^*,\\ y'(t) = g (t, y(t)), & y(t_0) = x^{**}, \end{cases} \end{equation*} in the space of all bounded and continuous real functions on $[0,+\infty[$. We use best proximity point methods and measure of noncompactness theory under suitable assumptions on $f$ and $g$. Some new best proximity point theorems play a key role in the above result.

Citation

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Moosa Gabeleh. Calogero Vetro. "A best proximity point approach to existence of solutions for a system of ordinary differential equations." Bull. Belg. Math. Soc. Simon Stevin 26 (4) 493 - 503, november 2019. https://doi.org/10.36045/bbms/1576206350

Information

Published: november 2019
First available in Project Euclid: 13 December 2019

zbMATH: 07167739
MathSciNet: MR4042396
Digital Object Identifier: 10.36045/bbms/1576206350

Subjects:
Primary: 34A12 , 47H09

Keywords: Best proximity point (pair) , cyclic (noncyclic) generalized condensing operator , strictly convex Banach space , system of differential equations

Rights: Copyright © 2019 The Belgian Mathematical Society

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Vol.26 • No. 4 • november 2019
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