Journal of Integral Equations and Applications
- J. Integral Equations Applications
- Volume 27, Number 2 (2015), 273-287.
Solvability of a general nonlinear integral equation in $L^1$ spaces by means of a measure of weak noncompactness
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.
J. Integral Equations Applications, Volume 27, Number 2 (2015), 273-287.
First available in Project Euclid: 9 September 2015
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Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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]
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