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

Meftah, Badreddine

Real Anal. Exch. 42, No. 2, 391-410 (2017).

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.

Reviewer: József Sándor (Cluj-Napoca)

MSC:

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

Keywords:

dynamic equations; time scale; integral inequality; Gamidov inequality

Citations:

Zbl 0722.39001; Zbl 1029.26014