On some Gamidov integral inequalities on time scales and applications. (English) Zbl 1401.26033

The Gamidov inequality may be written as
\[ u(t)\leq k+\int^t_0 g(s) u(s)\,ds+ \int^T_0 h(s)u(s)\,ds, \] where \(k\geq 0\) is a constant, an \(T\) is a positive real number. In [Tamkang J. Math. 33, No. 4, 353–358 (2002; Zbl 1029.26014)], B. G. Pachpatte gave an extension of this inequality. Motivated by these results, the author extends Gamidov’s inequality to time scales (first introduced by S. Hilger [Result. Math. 18, No. 1–2, 18–56 (1990; Zbl 0722.39001)]).
The obtained results can be used as tools in the study of certain properties of dynamical equations on time scales.


26D15 Inequalities for sums, series and integrals
26D20 Other analytical inequalities
26E70 Real analysis on time scales or measure chains
Full Text: DOI Euclid