Note on some nonlinear integral inequalities in two independent variables on time scales and applications

Abstract Our aim in this note is to investigate some nonlinear integral inequalities in two independent variables on time scales.The inequalities given here can be used as handy tools to study the properties of certain partial dynamic equations on time scales

On Stability and Stabilization of Perturbed Time Scale Systems with Gronwall Inequalities

In the paper, new nonlinear time scale integral inequalities are given. By means of the explicit integral bounds, we derive suffcient conditions for the uniform asymptotic stability of perturbed systems on time scales. In the sequel, basing on Lyapunov's direct method, we develop the required type of stability.В статье представлены новые нелинейные интегральные неравенства на временной шкале. С помощью явных интегральных оценок получены достаточные условия для равномерной асимптотической устойчивости возмущенных систем на временных шкалах. Далее, основываясь на прямом методе Ляпунова, разработан нужный тип стабильности

Čebyšev's Type Inequalities for Functions of Selfadjoint Operators in Hilbert Spaces

Some inequalities for continuous synchronous (asynchronous) functions of selfadjoint linear operators in Hilbert spaces, under suitable assumptions for the involved operators, are given