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<p>This study reports sharp solutions to the majorization, radius, and coefficient estimation problems for normalized subfamilies of spiral-like analytic functions. We introduce these new subfamilies of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\alpha \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation>-spiral functions, where <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\alpha \in (-\pi /2,\pi /2)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>α</mi> <mo>∈</mo> <mo stretchy="false">(</mo> <mo>-</mo> <mi>π</mi> <mo stretchy="false">/</mo> <mn>2</mn> <mo>,</mo> <mi>π</mi> <mo stretchy="false">/</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>, using the subordination principle alongside trigonometric sine and cosine functions. Application of the main results yields logarithmic and inverse coefficient bounds. Our findings bring improvements over some recent results while maintaining consistency with existing ones.</p>

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Sharp solutions to majorization, radius and coefficient problems for certain new subclasses of normalized spiral-like analytic functions

  • 期刊论文

  • 发表日期：

    2025年11月26日

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  • Manzoor Hussain

摘要

This study reports sharp solutions to the majorization, radius, and coefficient estimation problems for normalized subfamilies of spiral-like analytic functions. We introduce these new subfamilies of \(\alpha \) α -spiral functions, where \(\alpha \in (-\pi /2,\pi /2)\) α ∈ ( - π / 2 , π / 2 ) , using the subordination principle alongside trigonometric sine and cosine functions. Application of the main results yields logarithmic and inverse coefficient bounds. Our findings bring improvements over some recent results while maintaining consistency with existing ones.