In the present paper a solution of the generalizedquadratic functional equation$$f(kx+ y)+f(kx+sigma(y))=2k^{2}f(x)+2f(y),phantom{+} x,yin{E}$$ isgiven where $sigma$ is an involution of the normed space $E$ and$k$ is a fixed positive integer. Furthermore we investigate theHyers-Ulam-Rassias stability of the functional equation. TheHyers-Ulam stability on unbounded domains is also studied.Applic...

We establish alternative theorems for quadratic inequality systems. Consequently, we obtain Lagrange multiplier characterizations of global optimality for classes of non-convex quadratic optimization problems. We present a generalization of Dine’s theorem to a system of two homogeneous quadratic functions with a regular cone. The class of regular cones are cones K for which (K∪−K) is a subspace...

Our purpose in this paper is the generalization of notions quadratic and symplectic structures to case 3-(Hom)-$\rho$-Lie algebras. We describe some properties them by expressing related lemmas theorems. Also, we introduce concept 3-pre-(Hom)-$\rho$-Lie algebras define their representation.

The paper deals with the problem of nonlinear fuzzy observers for a class of continuous-time nonlinear systems, represented by Takagi-Sugeno models with local nonlinear terms. On the basis of the Lyapunov stability criterion and incremental quadratic inequalities, the sufficient LMI design conditions are outlined. Numerical example is given to illustrate the procedure and to validate the perfor...

X iv :m at h/ 04 06 10 8v 1 [ m at h. FA ] 6 J un 2 00 4 QUADRATIC REVERSES OF THE CONTINUOUS TRIANGLE INEQUALITY FOR BOCHNER INTEGRAL OF VECTOR-VALUED FUNCTIONS IN HILBERT SPACES SEVER S. DRAGOMIR Abstract. Some quadratic reverses of the continuous triangle inequality for Bochner integral of vector-valued functions in Hilbert spaces are given. Applications for complex-valued functions are prov...

Abstract: This paper is concerned with the problem of H∞ filtering for continuous-time nonlinear quadratic systems. The aim is to design a full order dynamic filter that can also contain quadratic terms. The strategy relies on the use of a quadratic Lyapunov function and an inequality condition that assures an H∞ performance bound for the augmented quadratic system, composed by the original sys...

We formulate natural conformally invariant conditions on a 4-manifold for the existence of a metric whose Schouten tensor satisfies a quadratic inequality. This inequality implies that the eigenvalues of the Ricci tensor are positively pinched.

We establish an inequality by quadratic estimations; the double inequality [Formula: see text] holds for [Formula: see text], where the constants [Formula: see text] and 32 are the best possible.

New relationships are enlightened between various quadratic matrix inequality conditions for stability of a scalar polynomial. It is namely shown how a recently published linear matrix inequality condition can be derived from Hermite and Lya-punov stability criteria.