One method for proving inequalities by computer.
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 type -inequalities for fractional derivatives.
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 bounds of restricted type for the Hardy operator minus the identity on the cone of radially decreasing functions
We find the norm of the Hardy operator minus the identity acting on the cone of radially decreasing functions on minimal Lorentz spaces (restricted type estimates).
Optimal embeddings of critical Sobolev-Lorentz-Zygmund spaces
We establish the embedding of the critical Sobolev-Lorentz-Zygmund space into the generalized Morrey space with an optimal Young function Φ. As an application, we obtain the almost Lipschitz continuity for functions in . O’Neil’s inequality and its reverse play an essential role in the proofs of the main theorems.
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....
Optimal weighted harmonic interpolations between Seiffert means
We provide a set of optimal estimates of the form (1-μ)/𝓐(x,y) + μ/ℳ (x,y) ≤ 1/ℬ(x,y) ≤ (1-ν)/𝓐(x,y) + ν/ℳ (x,y) where 𝓐 < ℬ are two of the Seiffert means L,P,M,T, while ℳ is another mean greater than the two.
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 for cosine and sine operator functions
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 type inequalities related to the generalized Baouendi-Grushin vector fields