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http://dx.doi.org/10.4134/CKMS.2010.25.3.373

THE GEOMETRIC CONVEXITY OF A FUNCTION INVOLVING GAMMA FUNCTION WITH APPLICATIONS  

Chu, Yuming (DEPARTMENT OF MATHEMATICS HUZHOU TEACHERS COLLEGE)
Zhang, Xiaoming (HAINING RADIO AND TV UNIVERSITY)
Zhang, Zhihua (ZIXING MUNICIPAL SCHOOL)
Publication Information
Communications of the Korean Mathematical Society / v.25, no.3, 2010 , pp. 373-383 More about this Journal
Abstract
In this paper, we prove that $(\Gamma(x))^{\frac{1}{x-1}}$ is geometrically convex on (0, $\infty$). As its applications, we obtain some new estimates for $\frac{[\Gamma(x+1)]^{\frac{1}{x}}} {[\Gamma(y+1)]^{\frac{1}{y}}}$.
Keywords
gamma function; geometrically convex function; geometrically concave function; monotonicity;
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