Estimates for initial coefficients of certain bi-univalent functions

Ajay Kumar; Vibha Madaan; V. Ravichandran

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Estimates for initial coefficients of certain bi-univalent functions

Vibha Madaan, Ajay Kumar, V. Ravichandran

Complex Variables · Submitted 21 Jun 2020

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Estimates are obtained for the initial coefficients of a normalized analytic function $f$ in the unit disk $\mathbb{D}$ such that $f$ and the analytic extension of $f^{-1}$ to $\mathbb{D}$ belong to certain subclasses of univalent functions.

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arXiv ID2006.11742 (version 1)

Pith IDFAH3ZSVM, Pith's permanent record of this paper and its review

CitationAjay Kumar, Vibha Madaan, V. Ravichandran. "Estimates for initial coefficients of certain bi-univalent functions." arXiv:2006.11742 (2020). https://pith.science/paper/FAH3ZSVM

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Estimates are obtained for the initial coefficients of a normalized analytic function $f$ in the unit disk $\mathbb{D}$ such that $f$ and the analytic extension of $f^{-1}$ to $\mathbb{D}$ belong to certain subclasses of univalent functions. The bounds obtained improve some existing known bounds.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Estimates are obtained for the initial coefficients of a normalized analytic function $f$ in the unit disk $\mathbb{D}$ such that $f$ and the analytic extension of $f^{-1}$ to $\mathbb{D}$ belong to certain subclasses of univalent functions.	contribution 0.79	0.90	0.49	asserted 1.00
s1	The bounds obtained improve some existing known bounds.	result 0.53	0.89	0.38	asserted 1.00

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Original abstract

Estimates are obtained for the initial coefficients of a normalized analytic function $f$ in the unit disk $\mathbb{D}$ such that $f$ and the analytic extension of $f^{-1}$ to $\mathbb{D}$ belong to certain subclasses of univalent functions. The bounds obtained improve some existing known bounds.

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States the same result 1 paper

Estimates for the initial coefficients are obtained for bi-univalent functions belonging to certain classes defined by subordination and relevant connections with earlier results are pointed out.

Estimates for the Initial Coefficients of Bi-univalent Functions · 0.92

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Compares with 1 paper

Moreover, the estimates so obtained are observed to be an improvement over the ones derived in [ref] .

On Coefficient problem for bi-univalent analytic functions · Introduction and Preliminaries · 0.99

Cites as background 1 paper

Bohra et al. [ref] and Ali et al. [ref] gave estimates on the coefficients $a_2$ and $a_3$ of the functions in the class $𝒮^*_σ(φ)$.

On Coefficient problem for bi-univalent analytic functions · Introduction and Preliminaries · 0.96

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