The paper presents an $L^{r}-$ analogue of an inequality regarding the $s^{th}$ derivative of a polynomial having zeros outside a circle of arbitrary radius but greater or equal to one. Our result provides improvements and generalizations of some well-known polynomial inequalities.

Among complex smooth projective threefolds with ample canonical divisor K, the Noether inequality is of the form K ≥ 4 3 pg − δ 3 where pg denotes the geometric genus of the threefold and δ is certain number in {10, 12, 14}. Introduction Suppose S is a smooth minimal projective surface of general type. It is well known that M. Noether ([N]) proved the inequality K S ≥ 2pg − 4 whence K 2 S ≥ 2χ−...

Some inequalities of Hermite-Hadamard type for h-convex functions de…ned on convex subsets in real or complex linear spaces are given. Applications for norm inequalities are provided as well. 1. Introduction The following inequality holds for any convex function f de…ned on R (1.1) (b a)f a+ b 2 < Z b a f(x)dx < (b a) + f(b) 2 ; a; b 2 R: It was …rstly discovered by Ch. Hermite in 1881 in the j...

In this paper we investigate the evolution of the inequality in well-being across di¤erent countries between 1975 and 2000. We treat well-being as a multidimensional concept focusing on three important dimensions of life: standard of living, health and education. Inequality in the three dimensions shows a di¤erent trend between 1975 and 2000. We propose a ‡exible measure of well-being and use t...

A geometric approach of Blundon’s inequality is presented. Theorem 2.1 gives the formula for cos ̂ ION in terms of the symmetric invariants s , R , r of a triangle, implying Blundon’s inequality (Theorem 2.2). A dual formula for cos ̂ IaONa is given in Theorem 3.1 and this implies the dual Blundon’s inequality (Theorem 3.2). As applications, some inequalities involving the exradii of the triangle...

In this paper, by introducing four parameters A,B,?,? and using the Euler-Maclaurin expansion for Riemann zeta function, we establish an inequality of a weight coefficient. Using inequality, derive generalizations Hilbert?s type inequality.

We prove a stability version of the Prékopa-Leindler inequality. 1 The problem Our main theme is the Prékopa-Leindler inequality, due to A. Prékopa [14] and L. Leindler [13]. Soon after its proof, the inequality was generalized in A. Prékopa [15] and [16], C. Borell [7], and in H.J. Brascamp, E.H. Lieb [8]. Various applications are provided and surveyed in K.M. Ball [1], F. Barthe [5], and R.J....

in this paper we consider the problem of delay-dependent robusth1 control for uncertain fuzzy systems with time-varying delay. the takagi–sugeno (t–s) fuzzy model is used to describe such systems. time-delay isassumed to have lower and upper bounds. based on the lyapunov-krasovskiifunctional method, a sufficient condition for the existence of a robust $h_{infty}$controller is obtained. the fuzz...

We construct a solution to inverse mean curvature flow on an asymptotically hyperbolic 3-manifold which does not have the convergence properties needed in order to prove a Penrose–type inequality. This contrasts sharply with the asymptotically flat case. The main idea consists in combining inverse mean curvature flow with work done by Shi–Tam regarding boundary behavior of compact manifolds. As...

Integral inequalities play critical roles in measure theory and probability theory. Given recent profound discoveries in the field of fuzzy set theory, fuzzy inequality has become a hot research topic in recent years. For classical Sandor type inequality, this paper intends to extend the Sugeno integral. Based on the (s,m)-convex function in the second sense, a new Sandor type inequality is pro...