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On certain subclasses of multivalently meromorphic close-to-convex maps

100%

Padmanabhan K.

Annales Polonici Mathematici

1998

tom 69

nr 3

251-263

Let Mₚ denote the class of functions f of the form $f(z) = 1/z^p + ∑_{k=0}^∞ aₖz^k$, p a positive integer, in the unit disk E = {|z| < 1}, f being regular in 0 < |z| < 1. Let $L_{n,p}(α) = {f: f ∈ Mₚ, Re{-(z^{p+1}/p) (Dⁿf)'} > α}$, α < 1, where $Dⁿf = (z^{n+p} f(z))^{(n)}/(z^p n!)$. Results on $L_{n,p}(α)$ are derived by proving more general results on differential subordination. These results reduce, by putting p =1, to the recent results of Al-Amiri and Mocanu.

A class of analytic functions defined by Ruscheweyh derivative

63%

Padmanabhan K., Jayamala M.

Annales Polonici Mathematici

1991

tom 54

nr 2

167-178

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.

Ograniczanie wyników

2 Annales Polonici Mathematici

2 Padmanabhan K.

1 Jayamala M.

1 1998

1 1991

Wyniki wyszukiwania

On certain subclasses of multivalently meromorphic close-to-convex maps

A class of analytic functions defined by Ruscheweyh derivative