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Radius Problems for Starlike Functions Associated with the Sine Function

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Abstract

Let \({\mathcal {S}}^*_s\) be the class of normalized analytic functions f defined on the unit disk such that the quantity \(zf'(z)/f(z)\) lies in an eight-shaped region in the right-half plane, which is the image of the unit disk under an entire function defined by \(\varphi (z)=1+\sin z\). For this class, we determine the \({\mathcal {S}}^*_s\)-radii for the class of Janowski starlike functions and some other geometrically defined classes. A relation between this class and the class of Janowski starlike functions is also discussed.

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Acknowledgements

The authors would like to express their gratitude to the referees for many valuable suggestions regarding a previous version of this paper. The first author was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (No. 2016R1D1A1A09916450).

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Authors and Affiliations

  1. Department of Applied Mathematics, Pukyong National University, Busan, 48513, Korea

    N. E. Cho & V. Kumar

  2. Department of Mathematics, Central University of Haryana, Haryana, 123031, India

    V. Kumar

  3. Department of Applied Mathematics, Delhi Technological University, Delhi, 110042, India

    S. S. Kumar

  4. Department of Mathematics, University of Delhi, Delhi, 110007, India

    V. Ravichandran

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  1. N. E. Cho
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  2. V. Kumar
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  3. S. S. Kumar
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  4. V. Ravichandran
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Correspondence to V. Kumar.

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Communicated by Ali Abkar.

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Cho, N.E., Kumar, V., Kumar, S.S. et al. Radius Problems for Starlike Functions Associated with the Sine Function. Bull. Iran. Math. Soc. 45, 213–232 (2019). https://doi.org/10.1007/s41980-018-0127-5

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  • DOI: https://doi.org/10.1007/s41980-018-0127-5

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