# On starlikeness of certain integral transforms

• Volume: 56, Issue: 3, page 227-232
• ISSN: 0066-2216

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## Abstract

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Let A denote the class of normalized analytic functions in the unit disc U = z: |z| < 1. The author obtains fixed values of δ and ϱ (δ ≈ 0.308390864..., ϱ ≈ 0.0903572...) such that the integral transforms F and G defined by $F\left(z\right)={\int }_{0}^{z}\left(f\left(t\right)/t\right)dt$ and $G\left(z\right)=\left(2/z\right){\int }_{0}^{z}g\left(t\right)dt$ are starlike (univalent) in U, whenever f ∈ A and g ∈ A satisfy Ref’(z) > -δ and Re g’(z) > -ϱ respectively in U.

## How to cite

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S. Ponnusamy. "On starlikeness of certain integral transforms." Annales Polonici Mathematici 56.3 (1992): 227-232. <http://eudml.org/doc/262314>.

@article{S1992,
abstract = {Let A denote the class of normalized analytic functions in the unit disc U = z: |z| < 1. The author obtains fixed values of δ and ϱ (δ ≈ 0.308390864..., ϱ ≈ 0.0903572...) such that the integral transforms F and G defined by $F(z) = ∫_0^z (f(t)/t)dt$ and $G(z) = (2/z) ∫_0^z g(t)dt$ are starlike (univalent) in U, whenever f ∈ A and g ∈ A satisfy Ref’(z) > -δ and Re g’(z) > -ϱ respectively in U.},
author = {S. Ponnusamy},
journal = {Annales Polonici Mathematici},
keywords = {subordination; convex function; starlike function; univalent function; analytic function; starlike univalent},
language = {eng},
number = {3},
pages = {227-232},
title = {On starlikeness of certain integral transforms},
url = {http://eudml.org/doc/262314},
volume = {56},
year = {1992},
}

TY - JOUR
AU - S. Ponnusamy
TI - On starlikeness of certain integral transforms
JO - Annales Polonici Mathematici
PY - 1992
VL - 56
IS - 3
SP - 227
EP - 232
AB - Let A denote the class of normalized analytic functions in the unit disc U = z: |z| < 1. The author obtains fixed values of δ and ϱ (δ ≈ 0.308390864..., ϱ ≈ 0.0903572...) such that the integral transforms F and G defined by $F(z) = ∫_0^z (f(t)/t)dt$ and $G(z) = (2/z) ∫_0^z g(t)dt$ are starlike (univalent) in U, whenever f ∈ A and g ∈ A satisfy Ref’(z) > -δ and Re g’(z) > -ϱ respectively in U.
LA - eng
KW - subordination; convex function; starlike function; univalent function; analytic function; starlike univalent
UR - http://eudml.org/doc/262314
ER -

## References

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1. [1] D. J. Hallenbeck and S. Ruscheweyh, Subordination by convex functions, Proc. Amer. Math. Soc. 52 (1975), 191-195. Zbl0311.30010
2. [2] S. S. Miller and P. T. Mocanu, Differential subordination and univalent functions, Michigan Math. J. 28 (1981), 157-171. Zbl0439.30015
3. [3] P. T. Mocanu, On starlikeness of Libera transform, Mathematica (Cluj) 28 (51) (1986), 153-155. Zbl0635.30013
4. [4] P. T. Mocanu, D. Ripeanu and M. Popovici, Best bound for the argument of certain analytic functions with positive real part, preprint, 'Babeş-Bolyai' Univ., Fac. Math., Res. Semin. 5 (1986), 91-98. Zbl0652.30011
5. [5] S. Ponnusamy, On a subclass of λ-spirallike functions, Mathematica (Cluj), to appear.
6. [6] S. Ponnusamy and V. Karunakaran, Differential subordination and conformal mappings, Complex Variables Theory Appl. 11 (1989), 79-86. Zbl0628.30009
7. [7] M. S. Robertson, An extremal problem for functions with positive real part, Michigan Math. J. 11 (1964), 327-335. Zbl0145.31502
8. [8] R. Singh and S. Singh, Starlikeness and convexity of certain integrals, Ann. Univ. Mariae Curie-Skłodowska Sect. A 35 (16) (1981), 145-148.

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