A Littlewood-Paley type inequality

In this note we prove the following theorem: Let u be a harmonic function in the unit ball and . Then there is a constant C = C(p, n) such that

A Noether type inequality

This paper gives a Noether type inequality of a minimal Gorenstein 3-fold of general type whose canonical map is generically finite.     

A set-valued type inequality system

A set-valued type inequality system is introduced along with two solvability questions composed of existence and perturbation, and main theorems are obtained, which include three necessary and sufficient conditions concerning the existence and a continuity property concerning the perturbation. As applications, two existence criteria with respect to a single-valued type inequality system have also been obtained.     

A general multidimensional Hermite-Hadamard type inequality

Using a stochastic approach, we establish a multidimensional version of the classical Hermite-Hadamard inequalities which holds for convex functions on general convex bodies. The result is closely related to the Dirichlet problem.     

A nonlinear inequality of Moser-Trudinger type

In this note, we will prove an inequality for almost plurisubharmonic functions on any K?hler-Einstein manifolds with positive scalar curvature. This inequality generalizes the stronger version of the so called Moser-Trudinger-Onofri inequality on , which was proved in [Au], and also refines a weaker inequality found by the first author in [T2]. Received: May 27, 1997 / Accepted: June 11, 1999     

Fisher information and Stam inequality on a finite group

We prove a discrete version of the Stam inequality for randomvariables taking values on a finite group.     

A Cauchy-Schwarz type inequality for fuzzy integrals

In this paper we prove a Cauchy-Schwarz type inequality for fuzzy integrals.     

A Liapunov type inequality for Sugeno integrals

The classical Liapunov inequality shows an interesting upper bound for the Lebesgue integral of the product of two functions. This paper proposes a Liapunov type inequality for Sugeno integrals. That is, we show that holds for some constant H_s,t,r where 0<t<s<r,f:[0,1]→[0,∞) is a non-increasing concave function, and μ is the Lebesgue measure on R. We also present two interesting classes of functions for which the classical Liapunov type inequality for Sugeno integrals with H_s,t,r=1 holds. Some examples are provided to illustrate the validity of the proposed inequality.     

A Chebyshev type inequality for fuzzy integrals

In this paper, we prove a Chebyshev type inequality for fuzzy integrals. More precisely, we show that:

where μ is the Lebesgue measure on and f,g:[0,1]→[0,∞) are two continuous and strictly monotone functions, both increasing or both decreasing. Also, some examples and applications are presented.     

A Cohen type inequality for Laguerre-Sobolev expansions

Let introduce the Sobolev type inner product

     

An application of the convolution inequality for the Fisher information

A characterization of the normal distribution by a statistical independence on a linear transformation of two mutually independent random variables is proved by using the convolution inequality for the Fisher information.     

A Nash type solution for hemivariational inequality systems

In this paper, we prove an existence result for a general class of hemivariational inequality systems using the Ky Fan version of the KKM theorem Fan (1984) [10] or Tarafdar fixed points Tarafdar (1987) [11]. As application, we give an infinite-dimensional version for the existence result of Nash generalized derivative points introduced recently by Kristály (2010) [5]. We also give an application to a general hemivariational inequality system.     

A Poincaré type inequality for Hessian integrals

In this paper we show that Hessian integrals , , can be estimated by those of higher order. The result extends a variant of the Poincaré inequality corresponding to the cases . The proof depends on solving a related non-linear parabolic initial boundary value problem. Received January 15, 1997 / Accepted March 1997     

A Feng Qi type inequality for Sugeno integral

In this paper, a Feng Qi type inequality for Sugeno integral is shown. The studied inequality is based on the classical Feng Qi type inequality for Lebesgue integral. Moreover, a generalized Feng Qi type inequality for Sugeno integral is proved with several examples given to illustrate the validity of the proposed inequalities.     

A Dunkl-Williams type inequality for absolute value operators

Dunkl and Williams showed that for any nonzero elements x,y in a normed linear space X