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math.CA2016
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…
math.CA2015★ 3 cited
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) }{…
math.CA2014
More convex functions by Artin`s method
Martin Himmel
First we recall the notion of conxity and log-convexity for real-valued. Then we generalize the trick used by Artin in his famous paper on the Gamma function to find log-convex sol…