<p>In this paper, a general subclass <InlineEquation ID="IEq1"> <EquationSource Format="TEX">${\mathcal {H}}_{{\Sigma }_m}^{h,p}(\lambda , \mu )$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msubsup> <mi mathvariant="script">H</mi> <mrow> <msub> <mi mathvariant="normal">Σ</mi> <mi>m</mi> </msub> </mrow> <mrow> <mi>h</mi> <mo>,</mo> <mi>p</mi> </mrow> </msubsup> <mrow> <mo stretchy="false">(</mo> <mi>λ</mi> <mo>,</mo> <mi>μ</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> of <i>m</i>-fold symmetric bi-univalent function is introduced. Estimates on the coefficients <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$|a_{m+1}|$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mrow> <mo stretchy="false">|</mo> </mrow> <msub> <mi>a</mi> <mrow> <mi>m</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mrow> <mo stretchy="false">|</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$|a_{2m+1}|$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mrow> <mo stretchy="false">|</mo> </mrow> <msub> <mi>a</mi> <mrow> <mn>2</mn> <mi>m</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mrow> <mo stretchy="false">|</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> for functions in the subclass <InlineEquation ID="IEq4"> <EquationSource Format="TEX">${\mathcal {H}}_{{\Sigma }_m}^{h,p}(\lambda ,\mu )$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msubsup> <mi mathvariant="script">H</mi> <mrow> <msub> <mi mathvariant="normal">Σ</mi> <mi>m</mi> </msub> </mrow> <mrow> <mi>h</mi> <mo>,</mo> <mi>p</mi> </mrow> </msubsup> <mrow> <mo stretchy="false">(</mo> <mi>λ</mi> <mo>,</mo> <mi>μ</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> are obtained. The results presented in this paper would generalize and improve some recent works of several earlier authors.</p>

Refinement of the coefficient problems for general subclass of m-fold symmetric bi-univalent functions

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发表日期：

2025年12月23日

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Ayyub Gorganli Davajii,
Ahmad Motamednezhad,
Safa Salehian,
Ágnes Orsolya Páll-Szabó

摘要

In this paper, a general subclass ${\mathcal {H}}_{{\Sigma }_m}^{h,p}(\lambda , \mu )$ $H_{Σ_{m}}^{h, p} (λ, μ)$ of m-fold symmetric bi-univalent function is introduced. Estimates on the coefficients $|a_{m+1}|$ $| a_{m + 1} |$ and $|a_{2m+1}|$ $| a_{2 m + 1} |$ for functions in the subclass ${\mathcal {H}}_{{\Sigma }_m}^{h,p}(\lambda ,\mu )$ $H_{Σ_{m}}^{h, p} (λ, μ)$ are obtained. The results presented in this paper would generalize and improve some recent works of several earlier authors.