Open Access
2016 Application of measure of noncompactness to Volterra equations of convolution type
Edgardo Alvarez, Carlos Lizama
J. Integral Equations Applications 28(4): 441-458 (2016). DOI: 10.1216/JIE-2016-28-4-441


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.


Download Citation

Edgardo Alvarez. Carlos Lizama. "Application of measure of noncompactness to Volterra equations of convolution type." J. Integral Equations Applications 28 (4) 441 - 458, 2016.


Published: 2016
First available in Project Euclid: 15 December 2016

zbMATH: 1355.45005
MathSciNet: MR3582797
Digital Object Identifier: 10.1216/JIE-2016-28-4-441

Primary: 34A12 , 45D05 , 45N05

Keywords: Darbo's fixed point theorem , measure of noncompactness , nonlinear functional integral equations , Volterra equations of convolution type

Rights: Copyright © 2016 Rocky Mountain Mathematics Consortium

Vol.28 • No. 4 • 2016
Back to Top