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Radius of starlikeness of certain analytic functions

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

We investigate radius problems for three classes of normalized analytic functions f characterized by its ratio with certain normalized analytic functions g. The first two classes consist of functions f satisfying \({\text {Re}} (f(z)/g(z))>0\) with either \({\text {Re}} (g(z)/s(z))>0\) or \({\text {Re}} (g(z)/s(z))>1/2\) and the other class consists of functions f satisfying \(\left|(f(z)/g(z))-1\right|<1\) with \({\text {Re}} (g(z)/s(z))>0\) for some starlike function s of order \(\alpha \), \(0\le \alpha <1\). For functions in these classes, we compute the various radii of starlikeness, including the radius of starlikeness of order \(\alpha \), and radius of Ma-Minda starlikeness associated with parabola, lemniscate of Bernoulli, exponential function, cardioid, sine, lune, rational function and nephroid.

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Acknowledgements

The authors are thankful to all three referees for their comments.

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  1. Department of Mathematics, National Institute of Technology, Tiruchirappalli, 620015, India

    S. Madhumitha & V. Ravichandran

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  1. S. Madhumitha
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  2. V. Ravichandran
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Correspondence to V. Ravichandran.

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The S. Madhumitha is supported by the institute fellowship from NIT Tiruchirappalli.

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Madhumitha, S., Ravichandran, V. Radius of starlikeness of certain analytic functions. Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 115, 184 (2021). https://doi.org/10.1007/s13398-021-01130-3

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  • DOI: https://doi.org/10.1007/s13398-021-01130-3

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