Optimum solutions for a system of differential equations via measure of noncompactness

New classes of mappings, called cyclic (noncyclic) condensing operators, are introduced and used to investigate the existence of best proximity points (best proximity pairs) with the help of a suitable measure of noncompactness. In this way, we obtain some real generalizations of Schauder and Darbo’...

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Bibliographic Details
Published in:Indagationes mathematicae 2018-06, Vol.29 (3), p.895-906
Main Authors: Gabeleh, M., Markin, J.
Format: Article
Language:English
Subjects:
Banach spaces
Best proximity point (pair)
Cyclic (noncyclic) condensing operator
Differential equations
Fixed points (mathematics)
Mapping
Mathematical analysis
Optimum solution
System of differential equations
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Summary:New classes of mappings, called cyclic (noncyclic) condensing operators, are introduced and used to investigate the existence of best proximity points (best proximity pairs) with the help of a suitable measure of noncompactness. In this way, we obtain some real generalizations of Schauder and Darbo’s fixed point theorems. In the last section, we apply such results to study the existence of optimum solutions to a system of differential equations.
ISSN:0019-3577
1872-6100
DOI:10.1016/j.indag.2018.01.008