Journal of Convex Analysis 21 (2014), No. 3, 765--783
Copyright Heldermann Verlag 2014
On Quasi-Gamma Functions
Teresa Bermúdez
Dep. de Análisis Matemático, Universidad de La Laguna, 38271 La Laguna - Tenerife, Spain
tbermude@ull.es
Antonio Martinón
Dep. de Análisis Matemático, Universidad de La Laguna, 38271 La Laguna - Tenerife, Spain
anmarce@ull.es
Kishin Sadarangani
Dep. de Matemáticas, Universidad de Las Palmas de Gran Canaria, Campus de Tafira Baja, 35017 Las Palmas de Gran Canaria, Spain
ksadaran@dma.ulpgc.es
[Abstract-pdf]
We define the quasi-gamma functions as the functions $f: ]0,\infty[ \longrightarrow ]0,\infty[$ such that $f(1)=1$, $f(x+1)=xf(x)$ for every $x>0$, and $f$ is quasi-convex. The main example of quasi-gamma function is the gamma function defined by Euler. We study some properties of the quasi-gamma functions and of the class ${\emph Q}$ of these functions.
Keywords: Gamma function, quasi-gamma function, quasi-convex function.
MSC: 26A51, 33B15, 52A41
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