Sanja Varošanec

Properties of h-convex functions related to the Hermite-Hadamard-Fejér inequalities

In this paper we prove the Hermite-Hadamard-Fejer inequalities for an h-convex function and we point out the results for some special classes of functions. Also, some generalization of the Hermite-Hadamard inequalities and some properties of functions H and F which are naturally joined to the h-convex function are given. Finally, applications on p-logarithmic mean and mean of the order p are obtained.

SUPERQUADRATIC FUNCTIONS AND REFINEMENTS OF SOME CLASSICAL INEQUALITIES

Using known properties of superquadratic functions we obtain a sequence of inequalities for superquadratic functions such as the convers and the reverse Jensentype inequalities, Giaccardis nad Petrovics inequality and Hermite-Hadamard inequality. Especially, when the superquadratic function is convex at the same time, then we get refinements of classical known results for convex functions. Some other properties of superquadratic functions are also given.

On some inequalities for h-concave functions

Abstract In this paper, some inequalities are proved for mappings whose p -th powers are h -concave functions by using the Godunova–Levin inequality, Holder’s inequality, Favard’s inequality, Chebyshev’s inequality and some other integral inequalities.

Gruss type inequalities in inner product modules

In this paper we give some properties of a generalized inner product in modules over H*-algebras and C*-algebras and we obtain inequalities of Griiss type.

Bessel and Grüss type inequalities in inner product modules

In this paper we give inequalities of Bessel type and inequalities of Gruss type in an inner product module over a proper H*-algebra or a C*-algebra.

Simpson's formula for functions whose derivatives belong to Lp spaces

Abstract In [1], Dragomir gave an inequality of Simpsons type for functions whose derivatives belong to L p spaces. Here, we generalize his results using functions whose n th derivatives, n ∈ {2, 3, 4}, belong to L p spaces.

An integral analogue of the Ostrowski inequality

We give an integral analogue of the Ostrowski inequality and several extensions, allowing in particular for multiple linear constraints

The Beckenbach-Dresher inequality in the Ψ-direct sums of spaces and related results

Let ψ̃:[0,1]→R be a concave function with ψ̃(0)=ψ̃(1)=1. There is a corresponding map .ψ̃ for which the inverse Minkowski inequality holds. Several properties of that map are obtained. Also, we consider the Beckenbach-Dresher type inequality connected with ψ-direct sums of Banach spaces and of ordered spaces. In the last section we investigate the properties of functions ψω,qand ∥.∥ω,q, (0 < ω < 1, q < 1) related to the Lorentz sequence space. Other posibilities for parameters ω and q are considered, the inverse Holder inequalities and more variants of the Beckenbach-Dresher inequalities are obtained.2000 MSC: Primary 26D15; Secondary 46B99.

SOME INTEGRAL INEQUALITIES, WITH APPLICATION TO BOUNDS FOR MOMENTS OF A DISTRIBUTION

1. IntroductionThe resolution of many problems in probability depends on being able to providesufficiently good upper or lower bounds to certain moments of distributions. Astriking example from the literature of a result that can offer such bounds was givenby P61ya over sixty years ago as the following theorem (see [7, Vol. II, p. 144] and[7, Vol. I, p. 94]).

Properties of some functionals associated with h-concave and quasilinear functions with applications to inequalities

We consider quasilinearity of the functional (h∘v)⋅(Φ∘gv), where Φ is a monotone h-concave (h-convex) function, v and g are functionals with certain super(sub)additivity properties. Those general results are applied to some special functionals generated with several inequalities such as the Jensen, Jensen-Mercer, Beckenbach, Chebyshev and Milne inequalities.