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
Coefficient Inequalities for Strongly Close-to-Convex Functions
✍ Scribed by William Ma; David Minda
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 189 KB
- Volume
- 205
- Category
- Article
- ISSN
- 0022-247X
No coin nor oath required. For personal study only.
✦ Synopsis
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 .
📜 SIMILAR VOLUMES
The class S H consists of harmonic, univalent, and sense-preserving functions f in the open unit disk U = z z < 1 , such that f = h + ḡ, where h z = z + ∞ n=2 a n z n and g z = ∞ n=1 a -n z n . Let S 0 H , C H , and C 0 H denote the subclass of S H with a -1 = 0, the subclass of S H with f being a c
## Abstract The object of the present paper is to prove some interesting sufficient conditions for __p__‐valently close‐to‐convex and starlike functions in the unit disk.
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.