Witold Jarczyk

On Mulholland’s inequality

H.P. Mulholland has presented a sufficient condition for a generalization of the Minkowski inequality and another such condition was given by R.M. Tardiff. We show that Mulhollands condition implies Tardiffs, but that the converse is false.

Reversible interval homeomorphisms

A characterization of continuously reversible self-mappings of an open interval, that is, compositions of two continuous involutions, is proved.

Also set-valued functions do not like iterative roots

In [1] Babbage studied (1.1) for f being the identity mapping. After him a lot of results concerning the general case of (1.1) in various settings have been proved. Many of them can be found in the monographs [12] and [13] by M. Kuczma and M. Kuczma, B. Choczewski, R. Ger, respectively, as well as in the book [19] by Gy. Targonski. Some recent results have been presented in the survey papers [3] and [2].

Generic properties of nonlinear functional equations

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Duplicating the cube and functional equations

In the present paper we consider a system of equations (1), (2) introduced in [2] in connection with the ancient Greek problem of duplicating the cube. We prove also some results in the case of a restricted domain, namely, if y = 2x:.1

Almost iterable functions

SummaryThe class of all self-mappings of a real compact interval which are iterable, i.e., embeddable in a continuous iteration semigroup, was characterized by M. C. Zdun in his paper [8]. Here we propose and characterize a slightly more general notion called almost iterability which (just as the notion of iterability) is motivated by problems in dynamics and stochastic processes.

A square iterative roots of some mean-type mappings

Abstract We determine all pairs of weighted quasi-arithmetic means being square iterative roots of another pair , that is we find all continuous strictly monotonic functions and parameters such that the equation is satisfied.

Convexity and a Stone-type theorem for convex sets in abelian semigroup setting

In this paper, two parallel notions of convexity of sets are introduced in the abelian semigroup setting. The connection of these notions to algebraic and to set-theoretic operations is investigated. A formula for the computation of the convex hull is derived. Finally, a Stone-type separation theorem for disjoint convex sets is established.

On some properties of strictly convex functions

We prove that some careless modification of the definition of strong convexity leads to a condition which is equivalent to that one of strict convexity. Mathematics subject classification (2010): 26A51, 39B62.

Proceedings of the 20th European conference on iteration theory

The 20th European Conference on Iteration Theory, ECIT 2014, was held on September 2014, 14–20, in Łagów, Poland. It was organized at Hotel Spa Morena by the Faculty of Mathematics, Computer Science and Econometrics of the University of Zielona Góra. ECIT 2014 followed the sequence of meetings started in Toulouse, France, 1973 and continued in Graz, Austria, 1977, Marburg, Germany, 1980, Toulouse 1982, Lochau, Austria, 1984, Caldes de Malavella, Spain, 1987, Batschuns, Austria, 1989, Lisboa, Portugal, 1991, Batschuns 1992, Opava, Czech Republic, 1994, Urbino, Italy, 1996, Muszyna, Poland, 1998, La Manga del Mar Menor, Spain, 2000, Evora, Portugal, 2002, Batschuns 2004, Gargnano, Italy, 2006, Yalta, Ukraine, 2008, Nant, France, 2010, Ponta Delgada, Portugal, 2012. The main topic of ECIT is iteration theory. This is a branch of mathematics and includes topics related to discrete dynamical systems, one-parameter semigroups of functions and functional equations. The aim of these theoretical studies is to model, analyze and understand iterative processes, for example systems with discrete time. Such systems arise in many different fields of application: engineering (e.g. control theory and electronics), physics, mechanics, economics, biology, ecology, and so on. All these questions have given rise to the introduction and the development of several branches of mathematics, related with iteration theory, as, for instance: