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<p>We introduce and study a class <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathcal{G}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">G</mi> </math></EquationSource> </InlineEquation>(<i>α, β</i>) comprising analytic functions associated with a sector domain, where <i>α, β</i> ∈ (0<i>,</i> 1]<i>.</i> By using the extended version of Jack’s lemma, we deduce the Open – Door lemma sufficient conditions for functions to be in <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathcal{G}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">G</mi> </math></EquationSource> </InlineEquation>(<i>α, β</i>)<i>.</i> Furthermore, we present special cases of our results that are in agreement with known results.</p>

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On Applications of the Extended Jack’s Lemma

  • 期刊论文

  • 发表日期：

    2025年11月4日

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  • S. Sivaprasad Kumar,
  • Pooja Yadav

摘要

We introduce and study a class \(\mathcal{G}\) G (α, β) comprising analytic functions associated with a sector domain, where α, β ∈ (0, 1]. By using the extended version of Jack’s lemma, we deduce the Open – Door lemma sufficient conditions for functions to be in \(\mathcal{G}\) G (α, β). Furthermore, we present special cases of our results that are in agreement with known results.