This analysis demonstrates sharp estimates of Taylor and logarithmic coefficients in analytic functions, suggesting important properties for classes of functions.
For 0≤ α≤ 1, let BS(α) be the class of all analytic functions in the unit disk D:=\~z:|z|<1\ with normalization $f(0)=0$ and $f'(0)=1$ that satisfy the subordinate relation zf'(z)/f(z)-1 z/(1-αz²) and BK(α) be the class of all functions f for which zf' ∈ BS(α). In this article, we obtain a sharp estimate of the initial Taylor coefficients and logarithmic coefficients for functions in the classes BS(α) and BK(α). Further, we obtain the radius of convexity and study the pre-Schwarzian norm for the classes BS(α) and BK(α).
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Ali et al. (2025) studied this question.
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