几类解析函数的对数系数

The Logarithmic Coefficients of Certain Classes of Analytic Functions

  • 摘要: 为进一步推进对数系数的估计研究,研究了几类解析函数B(λ, α, A, B, g(z)),B(λ, α, σ, g(z))和B(λ, α, σ)的对数系数|bn|:首先,利用从属关系给出了|(g(z)/f(z))α|的估计;其次,通过构造非负函数并结合复变函数模的积分估计方法,得到了B(λ, α, A, B, g(z))对数系数的上界表达式;最后,通过特例化参数,给出了B(λ, α, σ, g(z))和B(λ, α, σ)的对数系数估计。所建立的估计方法能有效获取上述函数类对数系数的最优上界,推广了已有经典结论。

     

    Abstract: To further advance the study on the estimation of logarithmic coefficients, the estimation of logarithmic coefficients |bn| is investigated for several classes of analytic functions B(λ, α, A, B, g(z)), B(λ, α, σ, g(z)) and B(λ, α, σ). First, an estimate for |(g(z)/f(z))α| is derived using subordination relations. Second, by constructing non-negative functions and employing integral estimation methods for the modulus of complex functions, an upper bound expression for the logarithmic coefficients of B(λ, α, A, B, g(z)) is established. Finally, through parameter specialization, explicit estimates for the logarithmic coefficients of B(λ, α, σ, g(z)) and B(λ, α, σ) are obtained. The established estimation method can effectively obtain the optimal upper bounds for the logarithmic coefficients of the aforementioned function classes, thereby extending the existing classical results.

     

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