# 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

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topRosihan 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

top- [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] 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] S. Ruscheweyh, Convolution in Geometric Function Theory, Les Presses de l'Université de Montréal, Montréal, 1982.

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