Chinese Annals of Mathematics, Series B

, Volume 40, Issue 4, pp 501–514

# Pseudo Asymptotically Periodic Solutions for Volterra Difference Equations of Convolution Type

• Zhinan Xia
Article

## Abstract

In this paper, the author studies the existence and uniqueness of discrete pseudo asymptotically periodic solutions for nonlinear Volterra difference equations of convolution type, where the nonlinear perturbation is considered as Lipschitz condition or non-Lipschitz case, respectively. The results are a consequence of application of different fixed point theorems, namely, the contraction mapping principle, the Leray-Schauder alternative theorem and Matkowski’s fixed point technique.

## Keywords

Pseudo asymptotically periodic function Volterra difference equations Contraction mapping principle Leray-Schauder alternative theorem

65Q10 35B40

## Notes

### Acknowledgement

The author would like to thank the anonymous referees for their careful reading of the manuscript and numerous suggestions for its improvement.

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