Geodesic
A class of analytic functions defined by Ruscheweyh derivative
Annales Polonici Mathematici, Tome 54 (1991) no. 2, pp. 167-178.

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The function $f(z) = z^p + ∑_{k=1}^{∞} a_{p+k} z^{p+k}$ (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 $K_{n+1,p}(h) ⊆ K_{n,p}(h)$ 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.
DOI : 10.4064/ap-54-2-167-178

K. Padmanabhan 1 ; M. Jayamala 1

1 
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K. Padmanabhan; M. Jayamala. A class of analytic functions defined by Ruscheweyh derivative. Annales Polonici Mathematici, Tome 54 (1991) no. 2, pp. 167-178. doi : 10.4064/ap-54-2-167-178. http://geodesic.mathdoc.fr/articles/10.4064/ap-54-2-167-178/

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