Since the last decade, there have been many literatures on qualitative properties of difference equations, those studies cover many branches of difference equations, see [3 7] and references therein.
One major role is determining a person's 'qualitative identity' because they control, wholly or in part, many of our qualitative properties.
There are many publications in the qualitative properties of solutions for these equations (see [6 9] and the references therein).
Especially, Berezansky et al. [6] proposed the following Nicholson's blowflies model with linear harvesting term: x'(t)=-delta x t)+px t-tau e^{-gamma x(t-tau)}-H(t-sigma). Since the work of Berezansky et al. [6], it has attracted much attention of many researchers to study the qualitative properties of the Nicholson's blowflies model with harvesting term.
Integral inequalities that give explicit bounds on unknown functions provide a very useful and important device in the study of many qualitative as well as quantitative properties of solutions of partial differential equations, integral equations, and integrodifferential equation.
The main application of the integral inequalities is that they provide an explicit bounds of the unknown functions, which are a very useful and important device in the study of many qualitative as well as quantitative properties of solutions of nonlinear differential equations.
(Qualitatively indiscernible entities share all their qualitative properties, while qualitative duplicates share only their intrinsic qualitative properties).
In recent years, the research of various mathematical inequalities has been paid much attention to by many authors, and many integral inequalities have been established, which provide handy tools for investigating the quantitative and qualitative properties of solutions of integral and differential equations.
Population models with stage structure have been investigated by many researchers, and various methods and techniques have been used to study the existence and qualitative properties of solutions [1 9].
