On a Coefficient Conjecture for Bazilevič Functions

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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Correspondence to Virendra Kumar.

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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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Keywords

  • Univalent function
  • Bazilevič function
  • Coefficient estimate
  • Coefficient conjecture

Mathematics Subject Classification

  • 30C45
  • 30C50