Abstract

We define the quasi-gamma functions as the functions f:]0,∞[⟶]0,∞[f: ]0,\infty[ \longrightarrow ]0,\infty[ such that f(1)=1f(1)=1, f(x+1)=xf(x)f(x+1)=xf(x) for every x>0x>0, and ff 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 Q{\emph Q} of these functions.

Author information

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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

Keywords

  • Gamma function
  • quasi-gamma function
  • quasi-convex function

Mathematics Subject Classification

26A51, 33B15, 52A41

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Suggested citation

T. Bermúdez, A. Martinón, K. Sadarangani. “On Quasi-Gamma Functions.” Journal of Convex Analysis 21 (2014), No. 3, 765–783. https://doi.org/10.68381/jca21041

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Published by Heldermann Verlag, 2014. Rights now held by Banach Press LLC.