A class of analytic functions defined by Ruscheweyh derivative

K. S. Padmanabhan; M. Jayamala

Annales Polonici Mathematici, Tome 55 (1991), p. 167-178 / Harvested from The Polish Digital Mathematics Library

Résumé

The function $f (z) = z^{p} + \sum_{k = 1}^{\infty} a_{p + k} z^{p + k}$ (p ∈ ℕ = 1,2,3,...) analytic in the unit disk E is said to be in the class $K_{n, p} (h)$ if ( $D^{n + p} f) / (D^{n + p - 1} f) ≺ h$ , where $D^{n + p - 1} f = (z^{p}) / ({(1 - z)}^{p + n}) * f$ and h is convex univalent in E with h(0) = 1. We study the class $K_{n, p} (h)$ and investigate whether the inclusion relation $K_{n + 1, p} (h) \subseteq K_{n, p} (h)$ holds for p > 1. Some coefficient estimates for the class are also obtained. The class $A_{n, p} (a, h)$ of functions satisfying the condition $a * (D^{n + p} f) / (D^{n + p - 1} f) + (1 - a) * (D^{n + p + 1} f) / (D^{n + p} f) ≺ h$ is also studied.

Publié le : 1991-01-01

Zbl 0727.30013

EUDML-ID : urn:eudml:doc:262247

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     author = {K. S. Padmanabhan and M. Jayamala},
     title = {A class of analytic functions defined by Ruscheweyh derivative},
     journal = {Annales Polonici Mathematici},
     volume = {55},
     year = {1991},
     pages = {167-178},
     zbl = {0727.30013},
     language = {en},
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K. S. Padmanabhan; M. Jayamala. A class of analytic functions defined by Ruscheweyh derivative. Annales Polonici Mathematici, Tome 55 (1991) pp. 167-178. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv54z2p167bwm/

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