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

• Autorzy: K. S. Padmanabhan
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

meromorphic multivalently close-to-convex; differential subordination; convolution

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: 1998
• Tom: 69
• Numer: 3
• Strony: 251-263

Daty

wydano

1998

otrzymano

1997-10-09

Twórcy

autor

K. S. Padmanabhan

• M 73/2, 31st Cross Street, Besant Nagar, Madras 600 090, India

Bibliografia

• [1] H. Al-Amiri and P. T. Mocanu, On certain subclasses of meromorphic close-to-convex functions, Bull. Math. Soc. Sci. Math. Roumanie 38 (86) (1994), 3-15.
• [2] A. E. Livingston, Meromorphic multivalent close-to-convex functions, Trans. Amer. Math. Soc. 119 (1965), 167-177.
• [3] S. S. Miller and P. T. Mocanu, Second order differential inequalities in the complex plane, J. Math. Anal. Appl. 65 (1978), 289-305.
• [4] S. S. Miller and P. T. Mocanu, Differential subordinations and univalent functions, Michigan Math. J. 28 (1981), 167-171.
• [5] S. S. Miller and P. T. Mocanu, The theory and applications of second order differential subordinations, Studia Univ. Babeş-Bolyai Math. 34 (1989), 3-33.
• [6] C. Pommerenke, Univalent functions, Vandenhoeck and Ruprecht, Göttingen, 1975.
• [7] S. Ruscheweyh, Eine Invarianzeigenschaft der Basilevič-Funktionen, Math. Z. 134 (1973), 215-219.