‎Some improvements of Young inequality and its reverse for positive‎ ‎numbers with Kantorovich constant $K(t‎, ‎2)=frac{(1+t)^2}{4t}$‎ ‎are given‎. ‎Using these inequalities some operator inequalities and‎ ‎Hilbert-Schmidt norm versions for matrices are proved‎. ‎In‎ ‎particular‎, ‎it is shown that if $a‎, ‎b$ are positive numbers and‎ ‎$0 leqslant nu leqslant 1,$ then for all integers $ kgeqsl...

and Applied Analysis 3 which is called the general variational inequality, introduced and studied by Noor 19 . It has been shown that the minimum of a class of differentiable functions can be characterized by the general variational inequality of type 2.3 . B If g ≡ I, the identity operator, then 2.1 reduces to find u ∈ C and w ∈ A u such that 〈F u w,v − u〉 ≥ 0, ∀v ∈ C, 2.4 which is known as th...

In this paper, by using some classical Mulholland type inequality, Berezin symbols and reproducing kernel technique, we prove the power inequalities for number $ber(A)$ self-adjoint operators $A$ on ${H}(\Omega )$. Namely, inequality Hilbert space are established. By applying that $(ber(A))^{n}\leq C_{1}ber(A^{n})$ any positive operator

In this paper we describe an essential improvement of our recent algorithm for computing cohomology of Lie (super)algebra based on partition of the whole cochain complex into minimal subcomplexes. The improvement consists in replacing the arithmetic of rational numbers or integers by much cheaper arithmetic of modular field and using the inequality between the dimensions of cohomology computed ...

This paper considers H∞ performance for Markovian jump systems with Time-varying delays. The systems under consideration involve disturbance signal, Markovian switching and timevarying delays. By using a new Lyapunov-Krasovskii functional and a convex optimization approach, a delay-dependent stability condition in terms of linear matrix inequality (LMI) is addressed, which guarantee asymptotica...

1. J. Burbea, Sharp inequalities for holomorphic functions, Illinois J. Math. 31 (1987) 248–264. 2. T. Carleman, Zur Theorie der Minimalflächen, Math. Z. 9 (1921) 154–160. 3. P. L. Duren, Theory of H p Spaces, Academic Press, New York, 1970; reprinted by Dover, Mineola, NY, 2000. 4. T. W. Gamelin and D. Khavinson, The isoperimetric inequality and rational approximation, this MONTHLY 96 (1989) 1...

In order to show novel generalizations of mathematical inequality, fractional integral operators are frequently used. Fractional used simulate a broad range scientific as well engineering phenomena such elasticity, viscous fluid, fracture mechanics, continuous population, equilibrium, visco-elastic deformation, heat conduction problems, and others. this manuscript, we introduce some notions gen...

We wish to demonstrate here the following elementary inequality of the differential calculus. If a function satisfies the conditions {ƒ(*)} ^ 1 and {/(x)} 2 + {F-»(x)} ^ 1 for all x and for some positive integer n, then the latter inequality is valid also when n is replaced by any smaller positive integer. Tha t such an inequality might be true is suggested by the validity of a similar but more...

We prove a H\"older-type inequality for Hamiltonian diffeomorphisms relating the $C^0$ norm, norm of derivative, and Hofer/spectral norm. obtain as consequence that sufficiently fast convergence in metric forces convergence. The second theme our paper is study pseudo-rotations arise from Anosov-Katok method. As an application inequality, we rigidity result such pseudo-rotations.

Second-order necessary conditions are developed for an abstract nonsmooth control problem with mixed state-control equality and inequality constraints as well as a constraint of the form G(x, u) e T, where T is a closed convex set of a Banach space with nonempty interior. The inequality constraints g{s, x, u) < 0 depend on a parameter 5 belonging to a compact metric space S. The equality constr...