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.
Ostrowski type inequalities for isotonic linear functionals.
Ostrowski type inequalities from a linear functional point of view.
Ostrowski type inequalities in the Grushin plane.
Ostrowski type inequalities over balls and shells via a Taylor-Widder formula.
Ostrowski Type Inequalities over Spherical Shells
2000 Mathematics Subject Classification: 26D10, 26D15.Here are presented Ostrowski type inequalities over spherical shells. These regard sharp or close to sharp estimates to the difference of the average of a multivariate function from its value at a point.
Ostrowski-Grüss type inequalities in two dimensions.
Ostrowski’s type inequalities for complex functions defined on unit circle with applications for unitary operators in Hilbert spaces
Some Ostrowski’s type inequalities for the Riemann-Stieltjes integral of continuous complex valued integrands defined on the complex unit circle and various subclasses of integrators of bounded variation are given. Natural applications for functions of unitary operators in Hilbert spaces are provided as well.