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<p>We introduce and study two new subclasses of the function class Σ of bi-univalent functions defined in the open unit disk and associated with the Sălăgean and <i>q</i>-derivative operators. Furthermore, we find estimates for the Taylor–Maclaurin coefficients <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\left|{a}_{2}\right|\)</EquationSource> <EquationSource Format="MATHML"><math> <mfenced close="|" open="|"> <msub> <mi>a</mi> <mn>2</mn> </msub> </mfenced> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\left|{a}_{3}\right|\)</EquationSource> <EquationSource Format="MATHML"><math> <mfenced close="|" open="|"> <msub> <mi>a</mi> <mn>3</mn> </msub> </mfenced> </math></EquationSource> </InlineEquation> of the functions from these new subclasses. The accumulated results are quite interesting and new.</p>

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Coefficient Estimates in New Subclasses of Analytic and Bi-Univalent Functions Defined by the Combinations of the q-derivative and the Sălăgean Derivative Operator

  • 期刊论文

  • 发表日期：

    2026年2月1日

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  • Halit Orhan

摘要

We introduce and study two new subclasses of the function class Σ of bi-univalent functions defined in the open unit disk and associated with the Sălăgean and q-derivative operators. Furthermore, we find estimates for the Taylor–Maclaurin coefficients \(\left|{a}_{2}\right|\) a 2 and \(\left|{a}_{3}\right|\) a 3 of the functions from these new subclasses. The accumulated results are quite interesting and new.