We study the antieigenvectors of the generalized eigenvalue problem Af = λBf by using the concept of stationary vectors and then obtain an operator inequality complementary to Schwarz’s inequality in Hilbert space. AMS Mathematics Subject Classification (2000): 47A63,47A75

We establish a sharp trilinear inequality for the extension operator associated to the paraboloid in R3. Our proof relies on a recent generalisation of the classical Loomis–Whitney inequality.

This paper investigates the problem of state feedback H∞ control for singular systems through delta operator approach. Firstly, a bounded real lemma corresponding to a singular continuous system under the framework of the delta operator model is obtained. Then, the existence condition and explicit expression of a desirable H∞ controller for the singular delta operator system are presented. As s...

We give a Jensen’s operator inequality for strongly convex functions. As a corollary, we improve Hölder-McCarthy inequality under suitable conditions. More precisely we show that if Sp (A) ⊂ I ⊆ (1,∞), then 〈Ax, x〉 r ≤ 〈Ax, x〉 − r − r 2 (

We prove Hausdorff-Young inequality for the Fourier transform connected with Riemann-Liouville operator. We use this inequality to establish the uncertainty principle in terms of entropy. Next, we show that we can derive the Heisenberg-Pauli-Weyl inequality for the precedent Fourier transform.

In this paper, we prove the sharp function inequality for the multilinear commutator related to the singular integral operator with variable Calderón-Zygmund kernel. By using the sharp inequality, we obtain the Lnorm inequality for the multilinear commutator. 2000 Mathematics Subject Classification: 42B20, 42B25.

‎Some functional inequalities‎ ‎in variable exponent Lebesgue spaces are presented‎. ‎The bi-weighted modular inequality with variable exponent $p(.)$ for the Hardy operator restricted to non‎- ‎increasing function which is‎‎$$‎‎int_0^infty (frac{1}{x}int_0^x f(t)dt)^{p(x)}v(x)dxleq‎‎Cint_0^infty f(x)^{p(x)}u(x)dx‎,‎$$‎ ‎is studied‎. ‎We show that the exponent $p(.)$ for which these modular ine...

Inequalities on networks have played important roles in the theory of netwoks. We study several famous inequalities on networks such as Wirtinger’s inequality, Hardy’s inequality, Poincaré-Sobolev’s inequality and the strong isoperimetric inequality, etc. These inequalities are closely related to the smallest eigenvalue of weighted discrete Laplacian. We discuss some relations between these ine...

In this paper, we introduce and investigate a new class of meromorphic functions defined by a differential operator. For this class, we obtain coefficient inequality, distortion inequality, radius of close-to-convex, starlikeness and convexity, extreme points and integral means inequality.

Tsallis relative operator entropy is defined and then its properties are given. Shannon inequality and its reverse one in Hilbert space operators derived by T.Furuta [4] are extended in terms of the parameter of the Tsallis relative operator entropy. Moreover the generalized Tsallis relative operator entropy is introduced and then several operator inequalities are derived.