Gronwall-Bellman type integral inequalities for abstract Lebesgue integral
In the present paper, the authors establish some new linear integral inequalities of the Gronwall-Bellman type for scalar functions of several variables involving abstract Lebesgue (especially Lebesgue-Stieltjes) integrals. Some delay and advance effects appear in the considered inequalities. The proofs given in the paper depend on some earlier work of the second author of the present paper [J. Math. Anal. Appl. 202, No. 1, 183-193 (1996; Zbl 0859.26008)]. An illustrating example is also given to convey the sharpness of the established results.
integral inequalities of the Gronwall-Bellman type
scientific article; zbMATH DE number 1042731