Demonstratio Mathematica (May 2020)
Coefficient inequalities for a subclass of Bazilevič functions
Abstract
Let f be analytic in D={z:|z| < 1}{\mathbb{D}}=\{z:|z\mathrm{|\hspace{0.17em}\lt \hspace{0.17em}1\}} with f(z)=z+∑n=2∞anznf(z)=z+{\sum }_{n\mathrm{=2}}^{\infty }{a}_{n}{z}^{n}, and for α ≥ 0 and 0 < λ ≤ 1, let ℬ1(α,λ){ {\mathcal B} }_{1}(\alpha ,\lambda ) denote the subclass of Bazilevič functions satisfying |f′(z)(zf(z))1−α−1|<λ\left|f^{\prime} (z){\left(\frac{z}{f(z)}\right)}^{1-\alpha }-1\right|\lt \lambda for 0 < λ ≤ 1. We give sharp bounds for various coefficient problems when f∈ℬ1(α,λ)f\in { {\mathcal B} }_{1}(\alpha ,\lambda ), thus extending recent work in the case λ = 1.
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