Measure of noncompactness and a generalized Darbo’s fixed point theorem and its applications to a system of integral equations

Abstract Işık et al. (Mathematics 7:862, 2019) presented an interesting generalization of the Banach contraction principle. In this paper, motivated by Işık et al., we give a new extension of the well-known Darbo inequality in a Banach space. Our results provide several generalizations of the Darbo...

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Main Authors:	Vahid Parvaneh, Maryam Khorshidi, Manuel De La Sen, Hüseyin Işık, Mohammad Mursaleen
Format:	Article
Language:	English
Published:	SpringerOpen 2020-05-01
Series:	Advances in Difference Equations
Online Access:	http://link.springer.com/article/10.1186/s13662-020-02703-z

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spelling	doaj-23e147ded54a4461aa13b47cf0735ed82020-11-25T02:51:34ZengSpringerOpenAdvances in Difference Equations1687-18472020-05-012020111310.1186/s13662-020-02703-zMeasure of noncompactness and a generalized Darbo’s fixed point theorem and its applications to a system of integral equationsVahid Parvaneh0Maryam Khorshidi1Manuel De La Sen2Hüseyin Işık3Mohammad Mursaleen4Department of Mathematics, Gilan-E-Gharb Branch, Islamic Azad UniversityDepartment of Mathematics, Firouzabad Institute of Higher EducationInstitute of Research and Development of Processes, University of The Basque CountryDepartment of Mathematics, Muş Alparslan UniversityDepartment of Medical Research, China Medical University Hospital, China Medical University (Taiwan)Abstract Işık et al. (Mathematics 7:862, 2019) presented an interesting generalization of the Banach contraction principle. In this paper, motivated by Işık et al., we give a new extension of the well-known Darbo inequality in a Banach space. Our results provide several generalizations of the Darbo inequality. As an application, we study the existence of solutions for a system of functional integral equations in C [ 0 , T ] $C[0,T]$ . Finally, we expose a genuine example to support the effectiveness of our results.http://link.springer.com/article/10.1186/s13662-020-02703-z
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Vahid Parvaneh Maryam Khorshidi Manuel De La Sen Hüseyin Işık Mohammad Mursaleen
spellingShingle	Vahid Parvaneh Maryam Khorshidi Manuel De La Sen Hüseyin Işık Mohammad Mursaleen Measure of noncompactness and a generalized Darbo’s fixed point theorem and its applications to a system of integral equations Advances in Difference Equations
author_facet	Vahid Parvaneh Maryam Khorshidi Manuel De La Sen Hüseyin Işık Mohammad Mursaleen
author_sort	Vahid Parvaneh
title	Measure of noncompactness and a generalized Darbo’s fixed point theorem and its applications to a system of integral equations
title_short	Measure of noncompactness and a generalized Darbo’s fixed point theorem and its applications to a system of integral equations
title_full	Measure of noncompactness and a generalized Darbo’s fixed point theorem and its applications to a system of integral equations
title_fullStr	Measure of noncompactness and a generalized Darbo’s fixed point theorem and its applications to a system of integral equations
title_full_unstemmed	Measure of noncompactness and a generalized Darbo’s fixed point theorem and its applications to a system of integral equations
title_sort	measure of noncompactness and a generalized darbo’s fixed point theorem and its applications to a system of integral equations
publisher	SpringerOpen
series	Advances in Difference Equations
issn	1687-1847
publishDate	2020-05-01
description	Abstract Işık et al. (Mathematics 7:862, 2019) presented an interesting generalization of the Banach contraction principle. In this paper, motivated by Işık et al., we give a new extension of the well-known Darbo inequality in a Banach space. Our results provide several generalizations of the Darbo inequality. As an application, we study the existence of solutions for a system of functional integral equations in C [ 0 , T ] $C[0,T]$ . Finally, we expose a genuine example to support the effectiveness of our results.
url	http://link.springer.com/article/10.1186/s13662-020-02703-z
work_keys_str_mv	AT vahidparvaneh measureofnoncompactnessandageneralizeddarbosfixedpointtheoremanditsapplicationstoasystemofintegralequations AT maryamkhorshidi measureofnoncompactnessandageneralizeddarbosfixedpointtheoremanditsapplicationstoasystemofintegralequations AT manueldelasen measureofnoncompactnessandageneralizeddarbosfixedpointtheoremanditsapplicationstoasystemofintegralequations AT huseyinisık measureofnoncompactnessandageneralizeddarbosfixedpointtheoremanditsapplicationstoasystemofintegralequations AT mohammadmursaleen measureofnoncompactnessandageneralizeddarbosfixedpointtheoremanditsapplicationstoasystemofintegralequations
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Measure of noncompactness and a generalized Darbo’s fixed point theorem and its applications to a system of integral equations

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