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Sharp coefficient inequalities for certain subclasses of bi-univalent Bazilevi\v{c} functions

Amol Bhausaheb Patil
대한수학회 (The Korean Mathematical Society)|2022.01|대한수학회논문집 (Communications of the KMS)|제37권 제1호|pp. 113-123|DOI 10.4134/CKMS.c200468

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키워드

univalent functionAnalytic functionbi-univalent functionstar-like functionBazilevi\v{c} function
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초록

In the present paper, we introduce the subclasses $\mathfrak{B}_{1\Sigma}(\mu)$, $\mathrm{B}_{1\Sigma}(\mu,\gamma)$ and $\mathit{U}_{\Sigma}(\mu,\gamma)$ of bi-univalent Bazilevi\v{c} functions which are defined in the open unit disk $\mathbb{D}$. Further, we obtain sharp estimates on initial coefficients $a_2$, $a_3$, $a_4$ and also sharp estimate on the Fekete-Szeg\"{o} functional $a_3-k{a}_{2}^{2}$ for the functions belong to these subclasses.

Abstract

In the present paper, we introduce the subclasses $\mathfrak{B}_{1\Sigma}(\mu)$, $\mathrm{B}_{1\Sigma}(\mu,\gamma)$ and $\mathit{U}_{\Sigma}(\mu,\gamma)$ of bi-univalent Bazilevi\v{c} functions which are defined in the open unit disk $\mathbb{D}$. Further, we obtain sharp estimates on initial coefficients $a_2$, $a_3$, $a_4$ and also sharp estimate on the Fekete-Szeg\"{o} functional $a_3-k{a}_{2}^{2}$ for the functions belong to these subclasses.

참고문헌 (27)

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