THE GEOMETRIC CONVEXITY OF A FUNCTION INVOLVING GAMMA FUNCTION WITH APPLICATIONS

Title & Authors
THE GEOMETRIC CONVEXITY OF A FUNCTION INVOLVING GAMMA FUNCTION WITH APPLICATIONS
Chu, Yuming; Zhang, Xiaoming; Zhang, Zhihua;

Abstract
In this paper, we prove that $\small{(\Gamma(x))^{\frac{1}{x-1}}}$ is geometrically convex on (0, $\small{\infty}$). As its applications, we obtain some new estimates for $\small{\frac{[\Gamma(x+1)]^{\frac{1}{x}}} {[\Gamma(y+1)]^{\frac{1}{y}}}}$.
Keywords
gamma function;geometrically convex function;geometrically concave function;monotonicity;
Language
English
Cited by
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2.
A Class of Logarithmically Completely Monotonic Functions Associated with a Gamma Function, Journal of Inequalities and Applications, 2010, 2010, 1, 392431
3.
Logarithmically Complete Monotonicity Properties Relating to the Gamma Function, Abstract and Applied Analysis, 2011, 2011, 1
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