# Quotient mean, its invariance with respect to a quasi-arithmetic mean-type mapping, and some applications

Aequationes mathematicae

, Volume 82, Issue 3, pp 247–253

First Online: 12 July 2011Received: 15 February 2011Revised: 10 June 2011

Abstract

Under some conditions on the functions f and g defined in a real interval I the function$$Q^{f,g}x,y:=\left \frac{f}{g} ight ^{-1} \left \frac{fx} {gy} ight$$is a strict mean in I. We examine the invariance of this mean with respect to the weighted quasi-arithmetic mean type mapping generated by f and g.Mathematics Subject Classification 2010Primary 26E60 Secondary 39B22 KeywordsMean quotient mean invariant mean mean-type mapping iterations functional equation  Download to read the full article text

Author: Janusz Matkowski