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Some linear and nonlinear integral inequalities on time scales in two independent variables. (English) Zbl 1180.26020
Summary: We establish some linear and nonlinear integral inequalities of Gronwall-Bellman-Bihari type for functions with two independent variables on general time scales. The results are illustrated with examples, obtained by fixing the time scales to concrete ones. An estimation result for the solution of a partial delta dynamic equation is given as an application.

MSC:
26E70 Real analysis on time scales or measure chains
26D15 Inequalities for sums, series and integrals
45K05 Integro-partial differential equations
93C70 Time-scale analysis and singular perturbations in control/observation systems
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