Some New Delayed Volterra - Fredholm Type Integral Inequalities And Their Applications

As we all know, in the study of differential equations, intergal equations and finite difference equations, one has often to deal with certain inequalities, which provide explicit bounds on the unknown functions. With the development of the differential equation theory in various disciplines in recent decades, integral inequalities have been more perfect promoted and become an important issue to promote mathematical research.The Gronwall-Bellman inrquality and its various generalizations play a fundamental role in the discussion of existence, boundedness and other properties of solutions of differential and integral equations. Some delay Volterra type integral inequations are needed to handle differential and integral equations with retardation. Some scholars and investigators have established some useful delay Volterra type integral inequalities in the past few years to achieve different goals. Pachpatte has established the following useful linear Volterra-Fredholm type integral inequalities with retardation.(?)This paper on the basis of the integral inequality and spreads the relevant integral inequality extended to some new integral inequalities, we study these inequalities from one variable and two variables, then get some new results.The thesis is divided into three chapters according to the contents.Chapter 1 Preference, we introduce the main contents and its background of this paper.Chapter 2 In the following we establish the retarded Volterra-Fredholm type integral inequalities of one variable and extended them to the following integral inequality.(?)Chapter 3 In this section, we apply our above results to the qualitative analysis of solutions to the new retarded Volterra-Fredholm type integral equations.