A class of analytic functions defined by Ruscheweyh derivative
Annales Polonici Mathematici, Tome 54 (1991) no. 2, pp. 167-178
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences
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.
@article{10_4064_ap_54_2_167_178,
author = {K. Padmanabhan and M. Jayamala},
title = {A class of analytic functions defined by {Ruscheweyh} derivative},
journal = {Annales Polonici Mathematici},
pages = {167--178},
year = {1991},
volume = {54},
number = {2},
doi = {10.4064/ap-54-2-167-178},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/ap-54-2-167-178/}
}
TY - JOUR AU - K. Padmanabhan AU - M. Jayamala TI - A class of analytic functions defined by Ruscheweyh derivative JO - Annales Polonici Mathematici PY - 1991 SP - 167 EP - 178 VL - 54 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.4064/ap-54-2-167-178/ DO - 10.4064/ap-54-2-167-178 LA - en ID - 10_4064_ap_54_2_167_178 ER -
%0 Journal Article %A K. Padmanabhan %A M. Jayamala %T A class of analytic functions defined by Ruscheweyh derivative %J Annales Polonici Mathematici %D 1991 %P 167-178 %V 54 %N 2 %U http://geodesic.mathdoc.fr/articles/10.4064/ap-54-2-167-178/ %R 10.4064/ap-54-2-167-178 %G en %F 10_4064_ap_54_2_167_178
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
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