Aequationes mathematicae

, Volume 79, Issue 3, pp 203–212

Generalized weighted quasi-arithmetic means

Article

DOI: 10.1007/s00010-010-0001-x

Cite this article as:
Matkowski, J. Aequat. Math. (2010) 79: 203. doi:10.1007/s00010-010-0001-x

Abstract

Under some natural assumptions on real functions f and g defined on a real interval I, we show that a two variable function Mf,g : I2I defined by
$$M_{f,g}(x,y)=(f+g)^{-1}(f(x)+g(y))$$
is a generalization of the quasi-arithmetic mean. Necessary and sufficient conditions for: symmetry, quasi-arithmeticity, weighted quasi-arithmeticity, homogeneity of Mf,g, as well as equality of two such means are presented.

Mathematics Subject Classification (2000)

Primary 26E3039B22

Keywords

Meanweighted quasi-arithmetic meangeneralized weighted quasi-arithmetic meanPexider equationadditive function

Copyright information

© Birkhäuser / Springer Basel AG 2010

Authors and Affiliations

  1. 1.Faculty of Mathematics, Informatics and EconometricsUniversity of Zielona GóraZielona GóraPoland
  2. 2.Institute of MathematicsSilesian UniversityKatowicePoland