<p>In the present paper, we introduce a new subclass <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({\mathcal {H}}^{*}(\lambda , K,L),\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mmultiscripts> <mrow> <mi mathvariant="script">H</mi> </mrow> <mrow /> <mrow> <mrow /> <mo>∗</mo> </mrow> </mmultiscripts> <mrow> <mo stretchy="false">(</mo> <mi>λ</mi> <mo>,</mo> <mi>K</mi> <mo>,</mo> <mi>L</mi> <mo stretchy="false">)</mo> </mrow> <mo>,</mo> </mrow> </math></EquationSource> </InlineEquation> <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(0 \le \lambda \le 1,\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>0</mn> <mo>≤</mo> <mi>λ</mi> <mo>≤</mo> <mn>1</mn> <mo>,</mo> </mrow> </math></EquationSource> </InlineEquation> <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(-L \le K &lt; L \le 1,\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>-</mo> <mi>L</mi> <mo>≤</mo> <mi>K</mi> <mo>&lt;</mo> <mi>L</mi> <mo>≤</mo> <mn>1</mn> <mo>,</mo> </mrow> </math></EquationSource> </InlineEquation> of harmonic univalent functions associated with Janowski function defined by subordination. We obtain necessary and sufficient conditions and properties such as distortion bounds, compactness, extreme points and integral mean inequalities for this new class of functions. Radii of convexity and starlikeness are also determined. </p>

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On Certain New Subclass of Janowski Harmonic Univalent Functions Defined Using Subordination

  • R. Sathish Srinivasan,
  • S. Porwal,
  • R. Ezhilarasi,
  • T. V. Sudharsan

摘要

In the present paper, we introduce a new subclass \({\mathcal {H}}^{*}(\lambda , K,L),\) H ( λ , K , L ) , \(0 \le \lambda \le 1,\) 0 λ 1 , \(-L \le K < L \le 1,\) - L K < L 1 , of harmonic univalent functions associated with Janowski function defined by subordination. We obtain necessary and sufficient conditions and properties such as distortion bounds, compactness, extreme points and integral mean inequalities for this new class of functions. Radii of convexity and starlikeness are also determined.