3 citations · 3 across the 2 of their papers we have counts for
6 papers · 1 filter
Means in money exchange operations
Jacek Bojarski, Janusz Matkowski
It is observed that in some money exchange operations, the applied -variable mean should be self reciprocally-conjugate, i.e. it should satisfy the equality \[ M\left( x_{1…
Invariant means and iterates of mean-type mappings
Janusz Matkowski, Paweł Pasteczka
Classical result states that for two continuous and strict means ( is an interval) there exists a unique -invariant mean , i.…
Invariance in a class of operations related to weighted quasi-geometric means
Jimmy Devillet, Janusz Matkowski
Let be an interval that is closed with respect to the multiplication. The operations of the form \begin{equation*} C_{f,g}…
A new invariance identity and means
Jimmy Devillet, Janusz Matkowski
The invariance identity involving three operations of the form \begin{equation*} D_{f,g}\left( x,y\right) =\left( f\circ g\right) ^{-1}\left( f\lef…
Homogeneous Beta-type functions
Martin Himmel, Janusz Matkowski
All beta-type functions, which are p-homogeneous, are determined. Applying this result, we show that a beta-type function is a homogeneous mean iff it is the harmonic one. A reform…
Directional convexity and characterizations of Beta and Gamma functions
Martin Himmel, Janu sz Matkowski
The logarithmic convexity of restrictions of the Beta functions to rays parallel to the main diagonal and the functional equation \[ ϕ\left( x+1\right) =\frac{x\left( x+k\right) }{…