A class of analytic functions defined by Ruscheweyh derivative

• Autorzy: K. S. Padmanabhan , M. Jayamala
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 30C45: Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1991
• Tom: 54
• Numer: 2
• Strony: 167-178

Daty

wydano

1991

otrzymano

1989-12-11

Twórcy

autor

K. S. Padmanabhan

• Ramanujan Institute, University of Madras, Madras 600 005, India

autor

M. Jayamala

• Department of Mathematics, Queen Mary's College, Madras 600 004, India

Bibliografia

• [1] P. Eenigenburg, S. S. Miller, P. T. Mocanu and M. O. Reade, On a Briot-Bouquet differential subordination, in: General Inequalities 3, Birkhäuser, Basel 1983, 339-348.
• [2] R. M. Goel and N. S. Sohi, A new criterion for p-valent functions, Proc. Amer. Math. Soc. 78 (1980), 353-357.
• [3] S. Ruscheweyh, New criteria for univalent functions, Proc. Amer. Math. Soc. 49 (1975), 109-115.
• [4] T. Umezawa, Multivalently close-to-convex functions, Proc. Amer. Math. Soc. 8 (1957), 869-874.