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<p>In geometric function theory, the problem of finding coefficient bounds plays an important role. In the present paper, we consider the third Hankel determinant defined for the coefficients of a function <i>f</i> belonging to the classes <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathcal {M}\)</EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathcal {N}\)</EquationSource> </InlineEquation> of analytic functions associated with the number 3/2. The main aim is to give the sharp upper bounds of the third Hankel determinant for the two classes. The results improved many known outcomes and are the best possible.</p>

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Sharp Bounds on the Third Hankel Determinant for Certain Subclasses of Analytic Functions

  • 期刊论文

  • 发表日期：

    2026年3月5日

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  • Lei Shi,
  • Muhammad Arif

摘要

In geometric function theory, the problem of finding coefficient bounds plays an important role. In the present paper, we consider the third Hankel determinant defined for the coefficients of a function f belonging to the classes \(\mathcal {M}\) and \(\mathcal {N}\) of analytic functions associated with the number 3/2. The main aim is to give the sharp upper bounds of the third Hankel determinant for the two classes. The results improved many known outcomes and are the best possible.