s-Orlicz Convex Functions in Linear Spaces and Jensen's Discrete Inequality

Refinements of s-Orlicz Convex Functions in Normed Linear Spaces

Minimizing Discrete Convex Functions with Linear Inequality Constraints

A class of discrete convex functions that can efficiently be minimized has been considered by Murota. Among them are L\-convex functions, which are natural extensions of submodular set functions. We first consider the problem of minimizing an L\-convex function with a linear inequality constraint having a positive normal vector. We propose a polynomial algorithm to solve it based on a binary se...

An Inequality for a Linear Discrete Operator Involving Convex Functions

For the functional A[ f ] = ∑k=1 ak f (zk) , we give necessary and sufficient conditions over the real numbers zk , such that, the inequality A[ f ] 0 , holds for some classes of convex functions. Then, we deduce an inequality related to Alzer’s inequality and a weighted majorization inequality.

Order continuous linear functionals on non-locally convex Orlicz spaces

The space of all order continuous linear functionals on an Orlicz space L defined by an arbitrary (not necessarily convex) Orlicz function φ is described.

An inequality in Orlicz function spaces with Orlicz norm

We use Simonenko quantitative indices of an N -function Φ to estimate two parameters qΦ and QΦ in Orlicz function spaces L [0,∞) with Orlicz norm, and get the following inequality: BΦ BΦ−1 ≤ qΦ ≤ QΦ ≤ AΦ Aφ−1 , where AΦ and BΦ are Simonenko indices. A similar inequality is obtained in L[0, 1] with Orlicz norm.