Starlikeness of functions satisfying a differential inequality

Rosihan M. Ali; S. Ponnusamy; Vikramaditya Singh

Annales Polonici Mathematici (1995)

  • Volume: 61, Issue: 2, page 135-140
  • ISSN: 0066-2216

Abstract

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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.

How to cite

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Rosihan M. Ali, S. Ponnusamy, and Vikramaditya Singh. "Starlikeness of functions satisfying a differential inequality." Annales Polonici Mathematici 61.2 (1995): 135-140. <http://eudml.org/doc/262359>.

@article{RosihanM1995,
abstract = {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.},
author = {Rosihan M. Ali, S. Ponnusamy, Vikramaditya Singh},
journal = {Annales Polonici Mathematici},
keywords = {univalent; convex; starlike; close-to-convex functions; duality of Hadamard products},
language = {eng},
number = {2},
pages = {135-140},
title = {Starlikeness of functions satisfying a differential inequality},
url = {http://eudml.org/doc/262359},
volume = {61},
year = {1995},
}

TY - JOUR
AU - Rosihan M. Ali
AU - S. Ponnusamy
AU - Vikramaditya Singh
TI - Starlikeness of functions satisfying a differential inequality
JO - Annales Polonici Mathematici
PY - 1995
VL - 61
IS - 2
SP - 135
EP - 140
AB - 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.
LA - eng
KW - univalent; convex; starlike; close-to-convex functions; duality of Hadamard products
UR - http://eudml.org/doc/262359
ER -

References

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  1. [1] R. Fournier and S. Ruscheweyh, On two extremal problems related to univalent functions, Rocky Mountain J. Math. 24 (1994), 529-538. Zbl0818.30013
  2. [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. Zbl0311.30011
  3. [3] S. Ruscheweyh, Convolution in Geometric Function Theory, Les Presses de l'Université de Montréal, Montréal, 1982. 

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