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A NEW EXTENSION OF DARBO’S FIXED POINT THEOREM USING RELATIVELY MEIR–KEELER CONDENSING OPERATORS

Part of: General theory in ordinary differential equations Nonlinear operators and their properties

Published online by Cambridge University Press:  19 July 2018

MOOSA GABELEH Open the ORCID record for MOOSA GABELEH [Opens in a new window]  and
CALOGERO VETRO Open the ORCID record for CALOGERO VETRO [Opens in a new window]
MOOSA GABELEH
Affiliation:
Department of Mathematics, Ayatollah Boroujerdi University, Boroujerd, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5746, Tehran, Iran email gab.moo@gmail.com, gabeleh@abru.ac.ir
CALOGERO VETRO*
Affiliation:
Department of Mathematics and Computer Science, University of Palermo, Via Archirafi 34, 90123, Palermo, Italy email calogero.vetro@unipa.it
*
✉calogero.vetro@unipa.it
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Abstract

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We consider relatively Meir–Keeler condensing operators to study the existence of best proximity points (pairs) by using the notion of measure of noncompactness, and extend a result of Aghajani et al. [‘Fixed point theorems for Meir–Keeler condensing operators via measure of noncompactness’, Acta Math. Sci. Ser. B35 (2015), 552–566]. As an application of our main result, we investigate the existence of an optimal solution for a system of integrodifferential equations.

Keywords

best proximity pointoptimal solutionrelatively Meir–Keeler condensing operatorstrictly convex Banach space

MSC classification

Primary: 47H10: Fixed-point theorems
Secondary: 47H09: Contraction-type mappings, nonexpansive mappings, $A$-proper mappings, etc. 34A12: Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 98 , Issue 2 , October 2018 , pp. 286 - 297
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

Footnotes

The first author was partially supported by a grant from the Institute for Research in Fundamental Sciences (IPM) (No. 96470046).

References

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