On a Coefficient Conjecture for Bazilevič Functions

  • Nak Eun Cho
  • Virendra KumarEmail author


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.


Univalent function Bazilevič function Coefficient estimate Coefficient conjecture 

Mathematics Subject Classification

30C45 30C50 



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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Copyright information

© Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2019

Authors and Affiliations

  1. 1.Department of Applied MathematicsPukyong National UniversityBusanSouth Korea
  2. 2.Department of Mathematics, Ramanujan CollegeUniversity of DelhiKalkaji, New DelhiIndia

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