On quasi-gamma functions
type: Item
instance of: scholarly article
zbMATH Open document ID: 1305.26025
author: T. Bermúdez
author: Antonio Martinón
author: K. Sadarangani
publication date: 2014-10-10T00:00:00Z
full work available at URL: jca21041.htm
Mathematics Subject Classification ID: 26A51
Mathematics Subject Classification ID: 33B15
Mathematics Subject Classification ID: 52A41
zbMATH DE Number: 6353710
zbMATH Keywords: gamma function
zbMATH Keywords: quasi-gamma function
zbMATH Keywords: quasi-convex function
MaRDI profile type: Publication
title: On quasi-gamma functions
published in: Journal of Convex Analysis
review text: A function \(f:(0,\infty)\to (0,\infty)\) is called quasi-gamma function, if it satisfies the following conditions: \(f(1)= 1\); \(f(x+1)= xf(x)\) \((x>0)\); and \(f\) is quasi-convex. The authors study properties of such functions, by proving e.g. that they are continuous, are \(\leq 1\) on \([1,2]\), are decreasing on \((0,1]\) and increasing on \([2,\infty)\). Further, they prove that the set of all quasi-gamma functions is not a convex set, and is topologically bounded in \(C(0,\infty)\). Some subclasses are also introduced and their study initiated.
reviewed by: József Sándor
description: scientific article; zbMATH DE number 6353710