Estimation of the solutions of Volterra difference equations

Abstract

Volterra equations, whose solution is defined by the whole previous history, are widely used in the modelling of the processes in continuous mechanics and biomechanics, problems of control and estimation and also some schemes of numerical solutions of integral and integral–differential equations [1–8]. In this connection, there is an essential interest in such properties of the solutions as stability, limiting periodicity, boundedness and various estimates of the solutions defined by the acting perturbations. In [9], such estimates were obtained for the solutions of nonlinear scalar integral Volterra equations of convolution type