We introduce the notion of strongly h-convex functions (defined on a normed space) and present some properties and representations of such functions. We obtain a characterization of inner product spaces involving the notion of strongly h-convex functions. Finally, a Hermite–Hadamard–type inequality for strongly h-convex functions is given.

2 Let H = [ M K K∗ N ] be a Hermitian matrix. It is known that the eigenvalues of M ⊕N are 3 majorized by the eigenvalues of H . If, in addition, H is positive semidefinite and the block K 4 is Hermitian, then the following reverse majorization inequality holds for the eigenvalues: 5

objective: to investigate maternal beliefs, practices about causes and determinant factors on drowning and maternal socioeconomic correlated factors on child mortality from drowning. m e t h od s : from march 2005 to march 2009, in a register-based cohort study and household survey, individual records utilizing drowning registry data of northern iran were enrolled.   mothers (n=276) who respond...

We show the existence of an absolute constant $\alpha>0$ such that, for every $k \geq 3$, $G:=\mathop{\mathrm{Sym}}(k)$, and $H \leqslant G$ index at least $3$, one has $|H/[H,H]| \leq |G:H|^{\alpha/ \log |G:H|}$. This inequality is best possible symmetric groups, we conjecture that it family arbitrarily large finite groups.

An optimal control problem for an elliptic variational inequality with a source term is considered. The obstacle is the control, and the goal is to keep the solution of the variational inequality close to the desired pro le while the H norm of the obstacle is not too large. The addition of the source term strongly a ects the needed compactness result for the existence of a minimizer.

In this paper we prove some inequalities for convex function of a higher order. The well known Hermite interpolating polynomial leads us to a converse of Jensen inequality for a regular, signed measure and, as a consequence, a generalization of Hadamard and Petrovi c's inequalities. Also, we obtain a new upper bound for the error function of the Hermite interpolating polynomial je H (x)j in ter...

In 1941, L. Ahlfors gave another proof of a 1933 theorem of H. Cartan on approximation to hyperplanes of holomorphic curves in Pn . Ahlfors’ proof built on earlier work of H. and J. Weyl (1938), and proved Cartan’s theorem by studying the associated curves of the holomorphic curve. This work has subsequently been reworked by H.-H. Wu in 1970, using differential geometry, M. Cowen and P. A. Grif...

If G is the fundamental group of a closed Riemannian manifold of negative curvature, then H n (1) (G; V) = 0 for all n 2 and for all Banach spaces V. This implies that the linear isoperimetric inequality is satissed for llings of higher dimensional real cycles. x1. Introduction. Hyperbolic groups in the sense of Gromov Gr] are known to be characterized as nitely presented groups G which satisfy...

In this paper we will prove an integral inequality of Stampacchia-type for a fourth-order elliptic operator on complete and connected Kähler manifolds. Our inequality implies a Hodge-Kodaira orthogonal decomposition for the Sobolev-type space W(X). In particular we will able to prove, under suitable topological conditions on the manifold X, the existence of an isomorphism between the Aeppli gro...