Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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THE GEOMETRIC CONVEXITY OF A FUNCTION INVOLVING GAMMA FUNCTION WITH APPLICATIONS

  • Received : 2007.11.06
  • Published : 2010.07.31
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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 $\frac{[\Gamma(x+1)]^{\frac{1}{x}}} {[\Gamma(y+1)]^{\frac{1}{y}}}$.

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