Starlikeness of functions satisfying a differential inequality

• Autorzy: Rosihan M. Ali , S. Ponnusamy , Vikramaditya Singh
• Języki publikacji: EN

Abstrakty

EN

In a recent paper Fournier and Ruscheweyh established a theorem related to a certain functional. We extend their result differently, and then use it to obtain a precise upper bound on α so that for f analytic in |z| < 1, f(0) = f'(0) - 1 = 0 and satisfying Re{zf''(z)} > -λ, the function f is starlike.

Słowa kluczowe

EN

univalent; convex; starlike; close-to-convex functions; duality of Hadamard products

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: 1995
• Tom: 61
• Numer: 2
• Strony: 135-140

Daty

wydano

1995

otrzymano

1993-10-12

poprawiono

1994-04-10

Twórcy

autor

Rosihan M. Ali

• School of Mathematics, Spic Science Foundation, 92 G.N. Chetty Road, Madras 600 017, India

autor

S. Ponnusamy

• 3A/95 Azad Nagar, Kanpur 208002, India

autor

Vikramaditya Singh

• School of Mathematical and Computer Sciences, Universiti Sains Malaysia, 11800 Penang, Malaysia

Bibliografia

• [1] R. Fournier and S. Ruscheweyh, On two extremal problems related to univalent functions, Rocky Mountain J. Math. 24 (1994), 529-538.
• [2] S. Ruscheweyh, Duality for Hadamard products with applications to extremal problems for functions regular in the unit disc, Trans. Amer. Math. Soc. 210 (1975), 63-74.
• [3] S. Ruscheweyh, Convolution in Geometric Function Theory, Les Presses de l'Université de Montréal, Montréal, 1982.