In this work, we estimate the bounds for the logarithmic coefficients \(\gamma _n\) of some well-known classes like \({\mathcal {F}}(c)\) for \(c\in (0,0.656]\cup \{2\}\). The best bound obtained for the logarithmic coefficient \(|\gamma _5|\) is sharp for \(c=2\). In a special case, it is important to note that we obtain the bounds for the logarithmic coefficients \(\gamma _n\) of the convex functions of order \(\alpha \) for some \(\alpha \). It is worthwhile mentioning that the given bounds would generalize some of the previous papers.

中文翻译：

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与凸函数有关的类的对数系数

在这项工作中，我们估计\（c \ in（0,0.656 ）为\（{\ mathcal {F}}（c）\）等一些知名类的对数系数\（\ gamma _n \）的边界] \ cup \ {2 \} \）。对数系数\（| \ gamma _5 | \）的最佳边界对于\（c = 2 \）来说是尖锐的。在特殊情况下，请注意我们得到的边界为对数系数\（\伽马_n \）的顺序的凸函数\（\阿尔法\）对于一些\（\阿尔法\） 。这是值得一提的是，给定的界限将概括一些以前的文件。