Abstract

We study the existence of discrete almost automorphic solutions and asymptotic behavior for non-linear Volterra difference equations of convolution type with infinite delay where the nonlinear perturbation is considered not necessarily globally Lipschitz. The results are a consequence of application of different fixed point theorems, namely, the contraction principle, the Leray-Schauder, the Krasnoselkii and Matkowski's fixed point technique. (C) 2013 Elsevier B.V. All rights reserved.