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On a Coefficient Conjecture for Bazilevič Functions

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Abstract

In this manuscript, a conjecture related to the estimate on the fifth coefficient of Bazilevič functions is settled for the range \(1\le \alpha \le \alpha ^*(\approx 2.049)\). However, for \(\alpha >\alpha ^*\), a non-sharp bound on the same is also derived. At the end of this manuscript, sharp upper bound on the functional \(|a_2a_3-a_4|\) is also obtained.

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Acknowledgements

The authors would like to express their gratitude to the referees for many valuable suggestions regarding the 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. 2019R1I1A3A01050861).

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Authors and Affiliations

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

    Nak Eun Cho

  2. Department of Mathematics, Ramanujan College, University of Delhi, Kalkaji, New Delhi, 110019, India

    Virendra Kumar

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  1. Nak Eun Cho
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  2. Virendra Kumar
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Correspondence to Virendra Kumar.

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Communicated by V. Ravichandran.

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Cho, N.E., Kumar, V. On a Coefficient Conjecture for Bazilevič Functions. Bull. Malays. Math. Sci. Soc. 43, 3083–3097 (2020). https://doi.org/10.1007/s40840-019-00857-y

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  • DOI: https://doi.org/10.1007/s40840-019-00857-y

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