On starlikeness of certain integral transforms

Volume 56 / 1992

S. Ponnusamy Annales Polonici Mathematici 56 (1992), 227-232 DOI: 10.4064/ap-56-3-227-232

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.

Authors

  • S. Ponnusamy

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