New Classes of Condensing Operators and Application to Solvability of Singular Integral Equations

Donal O'Regan

doi:10.2298/FIL2003843A

New Classes of Condensing Operators and Application to Solvability of Singular Integral Equations

Donal O'Regan

Mathematics

Iran University of Science and Technology

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

1 Citation (Scopus)

Abstract

In this paper, we introduce the notion of Krasnoselskii and Dugundji-Granas condensing operators in Banach spaces. In order to pave the way for a study the solvability of some classes of singular integral equations in the Banach algebra C[a , b], we provide some results for the existence of fixed points for such condensing operators. An example is presented to show the applicability of the results.

Original language	English (Ireland)
Pages (from-to)	843-860
Number of pages	18
Journal	Filomat
Volume	34
Issue number	3
DOIs	https://doi.org/10.2298/FIL2003843A
Publication status	Published - 1 Feb 2020

Keywords

Condensing operators
Darbo’s fixed point theorem
Measure of noncompactness
Singular integral equation

Authors (Note for portal: view the doc link for the full list of authors)

Authors
Aghajani, A,Aliaskari, M,O'Regan, D

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10.2298/FIL2003843A

Cite this

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title = "New Classes of Condensing Operators and Application to Solvability of Singular Integral Equations",

abstract = "In this paper, we introduce the notion of Krasnoselskii and Dugundji-Granas condensing operators in Banach spaces. In order to pave the way for a study the solvability of some classes of singular integral equations in the Banach algebra C[a , b], we provide some results for the existence of fixed points for such condensing operators. An example is presented to show the applicability of the results.",

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AB - In this paper, we introduce the notion of Krasnoselskii and Dugundji-Granas condensing operators in Banach spaces. In order to pave the way for a study the solvability of some classes of singular integral equations in the Banach algebra C[a , b], we provide some results for the existence of fixed points for such condensing operators. An example is presented to show the applicability of the results.

KW - Condensing operators

KW - Darbo’s fixed point theorem

KW - Measure of noncompactness

KW - Singular integral equation

UR - https://www.scopus.com/pages/publications/85097865185

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DO - 10.2298/FIL2003843A

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ER -

New Classes of Condensing Operators and Application to Solvability of Singular Integral Equations

Abstract

Keywords

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