• Communications of the Korean Mathematical Society
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• v.33 no.4
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• pp.1229-1237
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• 2018

In this paper, we obtain the coefficient bounds for subclass of meromorphic bi-univalent functions by using the Faber polynomial expansions. The results presented in this paper would generalize and improve some recent works.

• Bulletin of the Korean Mathematical Society
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• v.55 no.2
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• pp.405-413
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• 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.

• Journal of the Korean Mathematical Society
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• v.43 no.2
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• pp.413-424
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• 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 $E_M (G)$.

• Korean Journal of Mathematics
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• v.30 no.4
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• pp.629-642
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• 2022

In a recent paper, Sakar and Güney introduced a new class of bi-close-to-convex functions and determined the estimates for the general Taylor-Maclaurin coefficients of functions therein. The main purpose of this note is to give a generalization of this class. Also we point out the proof by Sakar and Güney is incorrect and present a correct proof.