A remark on quasiaffine functions

• Autorzy: Lewicki M.
• Języki publikacji: EN

Abstrakty

EN

We consider the functional inequality (*) min{f(x), f(y)} is less than or equal to f (rx + (1 - r)y) is less than or equal to max{f(x), f(y)}, where f is a real valued function on a linear space X and r is an element of (0, 1) is fixed. The purpose of the present paper is to investigate connections between functions satisfying inequality (*) and solutions of (*) with r = 1/2. As a conclusions we get, that under some regularity assumptions, function f is of the form f = g o alpha, where alpha : X approaches R is an additive and g : R approaches R is monotone.

Słowa kluczowe

EN

quasiaffine functions; functional equations; inequalities

PL

funkcje quasiafiniczne; równania funkcyjne; nierówności

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2006
• Tom: Vol. 39, nr 4
• Strony: 743--750
• Opis fizyczny: Bibliogr. 3 poz.

Twórcy

autor

Lewicki M.

• Institute of Mathematics Silesian University ul. Bankowa 14, 40-007 Katowice, Poland,

Bibliografia

• [1] M. Kuczma, An Introduction to the Theory of Functional Equations and Inequalities, PWN, Warsaw 1985.
• [2] S. Marcus, Sur une classe de fonctions définies par des inégalités introduite par M. Á. Császár, Acta Sci. Math. Szeged 19 (1958), 192–218.
• [3] K. Nikodem and Zs. Páles, A characterization of midpoint-quasiaffine functions, Publ. Math. Debrecen, 52/3–4(1998), 575–595.