Stability in functional difference equations with applications to infinite delay Volterra difference equations

Youssef N. Raffoul

doi:10.4134/BKMS.b180054

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Bull. Korean Math. Soc. 2018; 55(6): 1921-1930

Online first article November 7, 2018 Printed November 30, 2018

https://doi.org/10.4134/BKMS.b180054

Stability in functional difference equations with applications to infinite delay Volterra difference equations

Youssef N. Raffoul

University of Dayton

Abstract

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Abstract

We consider a functional difference equation and use fixed point theory to obtain necessary and sufficient conditions for the asymptotic stability of its zero solution. At the end of the paper we apply our results to nonlinear Volterra infinite delay difference equations.

Keywords: functional, discrete, fixed point, Lyapunov functionals, Volterra

MSC numbers: Primary 39A10, 39A11, 39A12