Submultiplicative and subadditive functions and integral inequalities of Bellman-Bihari type (Q1085292)

In this paper, two new function classes H and M, which contain the classes of nondecreasing submultiplicative functions and nondecreasing subadditive functions (say the classes A and B), respectively, are defined and studied in detail. Then, by using these new classes the author gives six theorems for Bellman-Bihari type nonlinear integral inequalities. The theorems obtained here are generalizations of many known integral inequalities involving some nonlinear nondecreasing submultiplicative or(and) subadditive functions.