Pál Burai

Extension Theorem for a Functional Equation

Abstract We are going to prove an extension theorem on a functional equation for special means studied by Domsta and Matkowski.

Necessary and sufficient condition on global optimality without convexity and second order differentiability

The main goal of this paper is to give a necessary and sufficient condition of global optimality for unconstrained optimization problems, when the objective function is not necessarily convex. We use Gâteaux differentiability of the objective function and its bidual (the latter is known from convex analysis).

Convexity with respect to families of sections and lines and their application in optimization

The main goal of this paper is to introduce two generalized convexity notions, to examine their properties and their use in optimization theory, in particular, to deduce necessary and sufficient first order conditions.

Comparability of Certain Homogeneous Means

We present some inequalities between two variables homogeneous means. Namely, we give necessary as well as sufficient condition on the comparability of Daroczy means.