Convergence Theorems for Varying Measures Under Convexity Conditions and Applications

Abstract In this paper, convergence theorems involving convex inequalities of Copson’s type (less restrictive than monotonicity assumptions) are given for varying measures, when imposing convexity conditions on the integrable functions or measures. Consequently, a continuous dependence result wide class differential equations with many interesting applications, namely measure (including Stieltjes equations, generalized problems, impulsive finitely countably impulses and also dynamic time scales) is provided.