Demonstratio Mathematica (May 2020)

Coefficient inequalities for a subclass of Bazilevič functions

  • Fitri Sa’adatul,
  • Marjono,
  • Thomas Derek K.,
  • Wibowo Ratno Bagus Edy

DOI
https://doi.org/10.1515/dema-2020-0040
Journal volume & issue
Vol. 53, no. 1
pp. 27 – 37

Abstract

Read online

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.

Keywords