General Fractional Opial Type Inequalities

A large variety of Lp(p 0) form very general Opial type inequalities arepresented engaging different order generalized fractional derivatives of a function. These arebased on a generalization of Taylors formula for generalized fractional derivatives. In the finalresults of this work, a monotonicity property of the involved function/highest-order generalizedfractional derivative is used.     

General Hardy type inequality for seminormed fuzzy integrals

Hardy type inequality for seminormed fuzzy integrals based on an aggregation function is studied in a rather general form. The main results of this paper generalize some previous results. Also, some conclusions are drawn and some problems for further investigations are given.     

A note on Opial and Wirtinger type discrete inequalities

The aim of the present note is to establish some new discrete inequalities of the Opial and Wirtinger type involving sequences of real numbers and their forward differences. The analysis used in the proofs is quite elementary and based on some simple observations and the applications of some fundamental inequalities.     

Opial type inequalities for cosine and sine operator functions

Various L _p form Opial type inequalities are given for cosine and sine operator functions with applications.     

Multidimensional weighted Opial inequalities

In this article we produce Opial-type weighted multidimensional inequalities over balls and arbitrary smooth bounded domains. The inequalities are sharp. The functions under consideration vanish on the boundary.     

Opial Type Inequalities for Semigroups

Various L_p form Opial type inequalities are given for semigroups with applications.     

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.     

Fuzzy Chebyshev type inequality

A Chebyshev type inequality for Sugeno integral is shown. Previous results of Flores-Franulič and Román-Flores [A. Flores-Franulič, H. Román-Flores, A Chebyshev type inequality for fuzzy integrals, Applied Mathematics and Computation 190 (2007) 1178–1184] are generalized. Several illustrated examples are given. As an application, a fuzzy Stolarsky’s inequality is obtained.     

A Fisher type inequality

In this paper we study subsets of a finite set that intersect each other in at most one element. Each subset intersects most of the other subsets in exactly one element. The following theorem is one of our main conclusions. Let S₁,… S_m be m subsets of an n-set S with |S₁| ? 2 (l = 1, …,m) and |S_i ∩ S_j| ? 1 (i ≠ j; i, j = 1, …, m). Suppose further that for some fixed positive integer c each S_i has non-empty intersection with at least m ? c of the remaining subsets. Then there is a least positive integer M(c) depending only on c such that either m ? n or m ? M(c).     

Whittle type inequality for demisubmartingales

A Whittle type inequality for demisubmartingales is derived and a strong law of large numbers for functions of a demisubmartingale is obtained.

     

An inequality of Schur's type

It is proved that the Chebyshev polynomial , has the greatest uniform norm on [−1, 1] of its third derivative among the real polynomials of degree at most n, which are bounded by 1 in [−1, 1] and vanish in −1 and 1. Research Supported by the Sofia University Science Foundation under Project No. 153/95.     

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.     

On a Littlewood-Paley type inequality

The following is proved: If is a function harmonic in the unit ball and if then the inequality

holds, where is the nontangential maximal function of This improves a recent result of Stoll. This inequality holds for polyharmonic and hyperbolically harmonic functions as well.

     

Orlicz序列空间的Opial性质

本文给出了Ｏｒｌｉｃｚ序列空间具有Ｏｐｉａｌ性质的条件，进而得到了具有Ｏｐｉａｌ条件的Ｏｒｌｉｃｚ序列空间中的任何一个非空的依坐标收敛闭的有界凸集上的第一类非扩张映射Ｔ必有不动点．     

Nikolskii type inequality for cardinal splines

The Nikolskii type inequality for cardinal splines

Note on an Iyengar type inequality

Using Hayashi’s inequality, an Iyengar type inequality for functions with bounded second derivative is obtained. This result improves a similar result from [N. Elezović, J. Pečarić, Steffensen’s inequality and estimates of error in trapezoidal rule, Appl. Math. Lett. 11 (6) (1998) 63–69] and, for some classes of functions, the result from [X.L. Cheng, The Iyengar type inequality, Appl. Math. Lett. 14 (2001) 975–978].