3 citations · 3 across the 1 of their papers we have counts for
4 papers
The logarithmic Cauchy quotient mean
Martin Himmel, Janusz Matkowski
Motivated by recent results on beta-type functions, a new family of means, which are of logarithmic Cauchy quotient type, are determined and characterized.
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.…
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) }{…