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Luor, Dah-Chin

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

Abstr. Appl. Anal. 2014, Article ID 973586, 8 p. (2014).
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.

MSC:

26D15 Inequalities for sums, series and integrals
26D10 Inequalities involving derivatives and differential and integral operators
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\textit{D.-C. Luor}, Abstr. Appl. Anal. 2014, Article ID 973586, 8 p. (2014; Zbl 1474.26123)
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References:

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