Logarithmic Convexity and Inequalities for the Gamma Function
✍ Scribed by Milan Merkle
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 132 KB
- Volume
- 203
- Category
- Article
- ISSN
- 0022-247X
No coin nor oath required. For personal study only.
✦ Synopsis
We propose a method, based on logarithmic convexity, for producing sharp Ž . Ž . bounds for the ratio ⌫ x q  r⌫ x . As an application, we present an inequality that sharpens and generalizes inequalities due to Gautschi, Chu, Boyd, Lazarevic-Ĺupas ¸, and Kershaw.
📜 SIMILAR VOLUMES
Many converses of Jensen's inequality for convex functions can be found in the literature. Here we give matrix versions, with matrix weights, of these inequalities. Some applications to the Hadamard product of matrices are also given. ᮊ 1997
## 2 3 Let f z s z q a z q a z q иии be a normalized strongly close-to-convex 2 3 function of order ␣ ) 0 defined on the unit disk .ބ This means that there is a normalized convex univalent function and  g ޒ such that X f z ␣ Ž .