Coefficient inequalities for a subclass of Bazilevič functions - Derek Thomas (Demonstratio Mathematica, 2020)
AbstractLet f be analytic in {\mathbb{D}}=\{z:|z\mathrm{|\hspace{0.17em}\lt \hspace{0.17em}1\}} with f(z)=z+{\sum }_{n=2}^{∞ }{a}_{n}{z}^{n}, and for α ≥ 0 and 0 < λ ≤ 1, let { {\mathcal B} }_{1}(α ,λ ) denote the subclass of Bazilevič functions satisfying \left|f^{′} (z){\left(\frac{z}{f(z)}\right)}^{1-α }-1\right|\lt λ for 0 < λ ≤ 1. We give sharp bounds for various coefficient problems when f\in { {\mathcal B} }_{1}(α ,λ ), thus extending recent work in the case λ = 1.