General theorems for stability and boundedness for nonlinear functional discrete systems (Q1874622)

The author considers the nonlinear functional discrete system \[ x(n+1)=G(n,x(s)),\qquad 0\leq s\leq n, \tag{*} \] where \(G: \mathbb{Z}^+\times \mathbb{R}^k \to \mathbb{R}^k\) is continuous in \(x\). The general theorems for stability and boundedness of the solutions of (*) are obtained by means of the discrete Lyapunov functionals.