On the utility of the Telyakovskiĭ's class .
On the weighted Ostrowski inequality.
On three inequalities similar to Hardy-Hilbert's integral inequality.
On Volterra inequalities and their applications.
On weak type inequalities for rare maximal functions
The properties of rare maximal functions (i.e. Hardy-Littlewood maximal functions associated with sparse families of intervals) are investigated. A simple criterion allows one to decide if a given rare maximal function satisfies a converse weak type inequality. The summability properties of rare maximal functions are also considered.
On weighted dyadic Carleson's inequalities.
On weighted Hardy and Poincaré-type inequalities for differences.
On weighted inequalities with geometric mean operator generated by the Hardy-type integral transform.
On weighted inequality of Hardy type for higher order derivatives
On weighted norm integral inequality of g. h. Hardy's type
On weighted Ostrowski type inequalities for operators and vector-valued functions.
On Young's inequality.
Opial inequalities on time scales
We present a version of Opial's inequality for time scales and point out some of its applications to so-called dynamic equations. Such dynamic equations contain both differential equations and difference equations as special cases. Various extensions of our inequality are offered as well.
Opial's type inequalities on time scales and some applications
We prove some new Opial type inequalities on time scales and employ them to prove several results related to the spacing between consecutive zeros of a solution or between a zero of a solution and a zero of its derivative for second order dynamic equations on time scales. We also apply these inequalities to obtain a lower bound for the smallest eigenvalue of a Sturm-Liouville eigenvalue problem on time scales. The results contain as special cases some results obtained for second order differential...
Optimal power mean bounds for the weighted geometric mean of classical means.
Optimal sublinear inequalities involving geometric and power means
There are many relations involving the geometric means and power means for positive -vectors . Some of them assume the form of inequalities involving parameters. There then is the question of sharpness, which is quite difficult in general. In this paper we are concerned with inequalities of the form and with parameters and We obtain a necessary and sufficient condition for the former inequality, and a sharp condition for the latter. Several applications of our results are also demonstrated....
Oscillatory integrals with polynomial phase.
Ostrowski, Grüss, Čebyšev type inequalities for functions whose second derivatives belong to and whose modulus of second derivatives are convex.
Ostrowski inequalities on time scales.
Ostrowski type inequalities for higher-order derivatives.