Volterra-Choquet integral equations

Sorin G. Gal

doi:10.1216/JIE-2019-31-4-495

Abstract

We study the classical Volterra integral equation of the second kind on an interval, in which the Lebesgue type integral is replaced by the more general Choquet integral with respect to a monotone, submodular and continuous from below and from above set function, including the so-called distorted Lebesgue measures.

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Sorin G. Gal. "Volterra-Choquet integral equations." J. Integral Equations Applications 31 (4) 495 - 504, 2019. https://doi.org/10.1216/JIE-2019-31-4-495

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Published: 2019

First available in Project Euclid: 6 February 2020

zbMATH: 07169458

MathSciNet: MR4060437

Digital Object Identifier: 10.1216/JIE-2019-31-4-495

Subjects:

Primary: 45B05

Secondary: 28A12 , 28A25 , 45G10 , 45L05

Keywords: Choquet integral , distorted Lebesgue measures , fixed point Theorem , monotone , submodular and continuous from below and from above set function , successive approximations , Volterra integral equation of second kind

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