Bounded solutions of discrete singular systems on infinite time intervals

This paper concerns noncausal, nonlinear discrete singular systems of the form
aX_{k+1} + Bx_{k} = m[x]_{k}
on the infinite interval
i = [0, 1, --.]
for some causal, nonlinear time variable operators
m
. Existence theorems for bounded solutions are given. Methods for estimating the infinite time problem by a finite time problem are developed.