Some Generalized Nonlinear Gamidov Type Integral Inequalities with Maxima in Two Variables and Their Weakly Singular Analogues

摘要

In this paper, some new nonlinear Gronwall-Bellman-Gamidov type integral inequalitieswith maxima in two variables and their weakly singular analogues are discussed. By usinganalysis techniques, such as change of variable, amplification method, differential and integration,inverse function, we estimated the upper bounds of the unknown functions. For illustratingthe validity of the inequalities established, some examples are given to study the boundednessand uniqueness of solutions of a certain Gamidov type weakly singular integral equations.