Several difference inequality and their applications

The main aim of this paper is to establish several general form difference inequalities, which contain both linear terms inside the sums and nonlinear terms inside twice nonlinear sums. We obtain some new results which provide explicit bounds on unknown functions. The inequalities given here can be used as tools in the study of boundedness, uniqueness, stability and boundary value problem of a difference equation. An example is given to illustrate the effectiveness of our results in estimation of solutions of some difference equations.