Real Economic Convergence in the EU Accession Countries

The paper aims to assess the real economic convergence among eight CEE countries that accessed the EU, as well as their convergence with the EU. Two aspects of convergence are analysed: (a) income convergence as a tendency to close the income gap; (b) cyclical convergence as a tendency to the conformity of business cycles. Income convergence is analysed in terms of ? and ? coefficients using regression equations between GDP per capita levels and GDP growth rates. Cyclical convergence is analysed using industrial production indexes and industrial confidence indicators. The analysis covers the period 1993-2004. The main findings may be summarised as follows: 1) CEE countries converge between themselves and towards the EU as regards the income level; 2) CEE countries reveal a good cyclical synchronisation with the EU; cyclical conformity within the region is better seen when the group is split into three subgroups: (a) Czech Republic, Slovakia and Slovenia, (b) Hungary and Poland, (c) the Baltic states. Both types of economic convergence are strongly affected by the dependence on the EU markets, including trade and capital flows.Economic Convergence, Economic Growth, Business Cycles, Economic Integration

Reducible means and reducible inequalities

It is well-known that if a real valued function acting on a convex set satisfies the $n$-variable Jensen inequality, for some natural number $n\geq 2$, then, for all $k\in\{1,\dots, n\}$, it fulfills the $k$-variable Jensen inequality as well. In other words, the arithmetic mean and the Jensen inequality (as a convexity property) are both reducible. Motivated by this phenomenon, we investigate this property concerning more general means and convexity notions. We introduce a wide class of means which generalize the well-known means for arbitrary linear spaces and enjoy a so-called reducibility property. Finally, we give a sufficient condition for the reducibility of the $(M,N)$-convexity property of functions and also for H\"older--Minkowski type inequalities

New generalized fuzzy metrics and fixed point theorem in fuzzy metric space

In this paper, in fuzzy metric spaces (in the sense of Kramosil and Michalek (Kibernetika 11:336-344, 1957)) we introduce the concept of a generalized fuzzy metric which is the extension of a fuzzy metric. First, inspired by the ideas of Grabiec (Fuzzy Sets Syst. 125:385-389, 1989), we define a new G-contraction of Banach type with respect to this generalized fuzzy metric, which is a generalization of the contraction of Banach type (introduced by M Grabiec). Next, inspired by the ideas of Gregori and Sapena (Fuzzy Sets Syst. 125:245-252, 2002), we define a new GV-contraction of Banach type with respect to this generalized fuzzy metric, which is a generalization of the contraction of Banach type (introduced by V Gregori and A Sapena). Moreover, we provide the condition guaranteeing the existence of a fixed point for these single-valued contractions. Next, we show that the generalized pseudodistance J:X×X→[0,∞) (introduced by Włodarczyk and Plebaniak (Appl. Math. Lett. 24:325-328, 2011)) may generate some generalized fuzzy metric NJ on X. The paper includes also the comparison of our results with those existing in the literature

A composite functional equation from algebraic aspect

In this paper we discuss the composite functional equation f(x+2f(y))=f(x)+y+f(y) on an Abelian group. This equation originates from Problem 10854 of the American Mathematical Monthly. We give an algebraic description of the solutions on uniquely 3-divisible Abelian groups, and then we construct all solutions f of this equation on finite Abelian groups without elements of order 3 and on divisible Abelian groups without elements of order 3 including the additive group of real numbers

On the invariance equation for two-variable weighted nonsymmetric Bajraktarevi\'c means

The purpose of this paper is to investigate the invariance of the arithmetic mean with respect to two weighted Bajraktarevi\'c means, i.e., to solve the functional equation $$\bigg(\frac{f}{g}\bigg)^{\!\!-1}\!\!\bigg(\frac{tf(x)+sf(y)}{tg(x)+sg(y)}\bigg) +\bigg(\frac{h}{k}\bigg)^{\!\!-1}\!\!\bigg(\frac{sh(x)+th(y)}{sk(x)+tk(y)}\bigg)=x+y \qquad(x,y\in I),$$ where $f,g,h,k:I\to\mathbb{R}$ are unknown continuous functions such that $g,k$ are nowhere zero on $I$, the ratio functions $f/g$, $h/k$ are strictly monotone on $I$, and $t,s\in\mathbb{R}_+$ are constants different from each other. By the main result of this paper, the solutions of the above invariance equation can be expressed either in terms of hyperbolic functions or in terms of trigonometric functions and an additional weight function. For the necessity part of this result, we will assume that $f,g,h,k:I\to\mathbb{R}$ are four times continuously differentiable

On a functional equation involving iterates and powers

We present a complete list of all continuous solutions f : (0,+∞)→(0,+∞) of the equation f 2(x) = γ [f (x)]αxβ, where α, β and γ > 0 are given real numbers