Journal of Integral Equations and Applications

Solvability of a general nonlinear integral equation in $L^1$ spaces by means of a measure of weak noncompactness

Fuli Wang

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Abstract

This paper is concerned with existence results for a quite general nonlinear functional integral equation in $L^1$ spaces. For this purpose, making use of the De Blasi measure of weak noncompactness, we first establish a new fixed point theorem of the nonautonomous superposition operators. After that, our theorem is applied to prove the solvability of the mentioned nonlinear functional integral equation.

Article information

Source
J. Integral Equations Applications, Volume 27, Number 2 (2015), 273-287.

Dates
First available in Project Euclid: 9 September 2015

Permanent link to this document
https://projecteuclid.org/euclid.jiea/1441790289

Digital Object Identifier
doi:10.1216/JIE-2015-27-2-273

Mathematical Reviews number (MathSciNet)
MR3395971

Zentralblatt MATH identifier
1323.47085

Subjects
Primary: 47H08: Measures of noncompactness and condensing mappings, K-set contractions, etc. 47H10: Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30] 47H30: Particular nonlinear operators (superposition, Hammerstein, Nemytskiĭ, Uryson, etc.) [See also 45Gxx, 45P05]

Keywords
Superposition operators measure of weak noncompactness fixed points nonlinear integral equations Banach algebras

Citation

Wang, Fuli. Solvability of a general nonlinear integral equation in $L^1$ spaces by means of a measure of weak noncompactness. J. Integral Equations Applications 27 (2015), no. 2, 273--287. doi:10.1216/JIE-2015-27-2-273. https://projecteuclid.org/euclid.jiea/1441790289


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