Generalized Nonlinear Volterra-Fredholm Type Integral Inequality with Two Variables

Abstract

We establish a class of new nonlinear retarded Volterra-Fredholm type integral inequalities, with two variables, where known function $w$ in integral functions in Q.-H. Ma and J. Pečarić, 2008 is changed into the functions $w_1,w_2$. By adopting novel analysis techniques, such as change of variable, amplification method, differential and integration, inverse function, and the dialectical relationship between constants and variables, the upper bounds of the embedded unknown functions are estimated. The derived results can be applied in the study of solutions of ordinary differential equations and integral equations.