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In this paper we study stability and boundedness of the nonlinear difference equation \begin{equation} x(t+1)=a(t)x(t)+c(t)\Delta x(t-g(t))+q(x(t),x(t-g(t))\big).\nonumber \end{equation} In particular we study equi-boundedness of solutions and the stability of the zero solution of this equation. Fixed point theorems are used in the analysis.