## Journal of Integral Equations and Applications

### Application of measure of noncompactness to Volterra equations of convolution type

#### Abstract

Sufficient conditions for the existence of at least one solution of a nonlinear integral equation with a general kernel are established. The existence result is proved in $C([0,T],E)$, where $E$ denotes an arbitrary Banach space. We use the Darbo-Sadovskii fixed point theorem and techniques of measure of noncompactness. We extend and generalize results obtained by other authors in the context of fractional differential equations. One example illustrates the theoretical results.

#### Article information

Source
J. Integral Equations Applications, Volume 28, Number 4 (2016), 441-458.

Dates
First available in Project Euclid: 15 December 2016

https://projecteuclid.org/euclid.jiea/1481792835

Digital Object Identifier
doi:10.1216/JIE-2016-28-4-441

Mathematical Reviews number (MathSciNet)
MR3582797

Zentralblatt MATH identifier
1355.45005

#### Citation

Alvarez, Edgardo; Lizama, Carlos. Application of measure of noncompactness to Volterra equations of convolution type. J. Integral Equations Applications 28 (2016), no. 4, 441--458. doi:10.1216/JIE-2016-28-4-441. https://projecteuclid.org/euclid.jiea/1481792835

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