• 대한수학회지
• /
• 제43권2호
• /
• pp.413-424
• /
• 2006

Let $\Gamma$ be a bounded rotation (BR) curve without cusps in the complex plane $\mathbb{C}$ and let G := int $\Gamma$. We prove that the rate of convergence of the interpolating polynomials based on the zeros of the Faber polynomials $F_n\;for\;\bar G$ to the function of the reflexive Smirnov-Orlicz class $E_M (G)$ is equivalent to the best approximating polynomial rate in $E_M (G)$.

• 대한수학회지
• /
• 제45권6호
• /
• pp.1535-1548
• /
• 2008

The analogues of Marcinkiewicz multiplier theorem and Littlewood-Paley theorem are proved for p-Faber series in weighted Smirnov spaces defined on bounded and unbounded components of a rectifiable Jordan curve.

• 대한수학회보
• /
• 제55권2호
• /
• pp.405-413
• /
• 2018

In this work, we use the Faber polynomial expansions to find upper bounds for the coefficients of analytic bi-univalent functions in subclass $\Sigma({\tau},{\gamma},{\varphi})$ which is defined by subordination conditions in the open unit disk ${\mathbb{U}}$. In certain cases, our estimates improve some of those existing coefficient bounds.

• Korean Journal of Mathematics
• /
• 제32권2호
• /
• pp.285-295
• /
• 2024

In this work, we consider the function $${\Psi}(z)=\frac{z}{\ln(1+z)}=1+\sum\limits_{n=1}^{\infty}\,G_nz^n$$ whose coefficients G_n are the Gregory coefficients related to Stirling numbers of the first kind and introduce a new subclass ${\mathcal{G}}^{{\lambda},{\mu}}_{\Sigma}(\Psi)$ of analytic bi-univalent functions subordinate to the function Ψ. For functions belong to this class, we investigate the estimates for the general Taylor-Maclaurin coefficients by using the Faber polynomial expansions. In certain cases, our estimates improve some of those existing coefficient bounds.