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.

中文翻译：

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关于Bazilevič函数的系数猜想

在此手稿中，有关Bazilevič函数第五个系数的估计的猜想针对范围\（1 \ le \ alpha \ le \ alpha ^ *（\ approx 2.049）\）被解决。但是，对于\（\ alpha> \ alpha ^ * \），也会推导在其上的非清晰边界。在该手稿的结尾，还获得了函数\（| a_2a_3-a_4 | \）的尖锐上限。