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Some convolution conditions for starlikeness and convexity of meromorphically multivalent functions

✍ Scribed by Jin-Lin Liu; H.M. Srivastava

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
188 KB
Volume
16
Category
Article
ISSN
0893-9659

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✦ Synopsis

By making use of the Hadamard product (or convolution), the authors derive necessary and sufficient conditions for a suitably normalized meromorphically p-valent function to be in the familiar classes of meromorphic p-valently starlike and meromorphic p-valently convex functions in the punctured unit disk.

πŸ“œ SIMILAR VOLUMES

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Let z be an analytic function with positive real part on ⌬ s z; z -1 with Ž . Ž . 0 s 1, Ј 0 ) 0 which maps the unit disk ⌬ onto a region starlike with respect Ž . to 1 and symmetric with respect to the real axis. Let ST denote the class of Ž . Ž . Ž . Ž . Ž . Ž . analytic functions f z with f 0 s

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✍ Neslihan UyanΔ±k; Melike Aydogan; Shigeyoshi Owa πŸ“‚ Article πŸ“… 2011 πŸ› Elsevier Science 🌐 English βš– 220 KB

## Starlike of order Ξ± Convex of order Ξ± a b s t r a c t For analytic functions f (z) in the open unit disk U, there are many sufficient conditions for f (z) to be starlike and convex in U. In view of the paper by P.T. Mocanu [P.T. Mocanu, Some starlikeness conditions for analytic functions, Rev.