On some vector-valued inequalities of Gronwall type. (English) Zbl 1474.26123

Summary: 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.


26D15 Inequalities for sums, series and integrals
26D10 Inequalities involving derivatives and differential and integral operators
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