In this paper we established some vector-valued inequalities of Gronwall type in ordered Banach spaces. Our results can be applied to investigate systems of real-valued Gronwall-type inequalities. We also show that the classical Gronwall-Bellman-Bihari integral inequality can be generalized from composition operators to a variety of operators, which include integral operators, maximal operators, geometric mean operators, and geometric maximal operators.
"On Some Vector-Valued Inequalities of Gronwall Type." Abstr. Appl. Anal. 2014 1 - 8, 2014. https://doi.org/10.1155/2014/973586