The Logarithmic Coefficients of Certain Classes of Analytic Functions

To further advance the study on the estimation of logarithmic coefficients, the estimation of logarithmic coefficients |b_n| 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.