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<p>In this paper, we first obtained some initial logarithmic coefficient bounds on a subclass of bounded turning functions associated with Bell numbers. For functions in this class, we determined the sharp bounds for the second Hankel determinant of logarithmic coefficients <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(H_{2,1}(F_{f}/2)\)</EquationSource> </InlineEquation> of bounded turning functions associated with Bell numbers. Furthermore, we calculated the bounds of third Hankel determinant of logarithmic coefficients <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(H_{3,1}(F_{f}/2)\)</EquationSource> </InlineEquation> of bounded turning functions subordinate to the function whose coefficients are Bell numbers. Finally, we calculated the third Hankel determinant of logarithmic coefficients of inverse functions.</p>

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Hankel determinants of logarithmic coefficients for the class of bounded turning functions associated with Bell numbers

  • 期刊论文

  • 发表日期：

    2025年10月27日

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  • Sevtap Sümer,
  • Gizem Nur Tufan

摘要

In this paper, we first obtained some initial logarithmic coefficient bounds on a subclass of bounded turning functions associated with Bell numbers. For functions in this class, we determined the sharp bounds for the second Hankel determinant of logarithmic coefficients \(H_{2,1}(F_{f}/2)\) of bounded turning functions associated with Bell numbers. Furthermore, we calculated the bounds of third Hankel determinant of logarithmic coefficients \(H_{3,1}(F_{f}/2)\) of bounded turning functions subordinate to the function whose coefficients are Bell numbers. Finally, we calculated the third Hankel determinant of logarithmic coefficients of inverse functions.