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- W3155332581 abstract "Abstract Let f be analytic in the unit disk D ={ z ∈ C : | z | < 1}, and S be the subclass of normalized univalent functions in D . We define the class of tilted bi-starlike functions <?CDATA ${S}_{sigma }^{* }(beta,delta )$?> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML overflow=scroll><mml:mrow><mml:msubsup><mml:mi>S</mml:mi><mml:mi>σ</mml:mi><mml:mo>*</mml:mo></mml:msubsup><mml:mo stretchy=false>(</mml:mo><mml:mi>β</mml:mi><mml:mo>,</mml:mo><mml:mspace width=0.25 /><mml:mi>δ</mml:mi><mml:mo stretchy=false>)</mml:mo></mml:mrow></mml:math> , which satisfy the condition <?CDATA $mathrm{Re}{{e}^{idelta}[frac{zf^{{prime}}(z)}{f(z)}]}gt beta $?> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML overflow=scroll><mml:mrow><mml:mi>Re</mml:mi><mml:mspace width=0.25 /><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>δ</mml:mi></mml:mrow></mml:msup><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mfrac><mml:mrow><mml:mi>z</mml:mi><mml:mi>f</mml:mi><mml:mo>'</mml:mo><mml:mo stretchy=false>(</mml:mo><mml:mi>z</mml:mi><mml:mo stretchy=false>)</mml:mo></mml:mrow><mml:mrow><mml:mi>f</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:mi>z</mml:mi><mml:mo stretchy=false>)</mml:mo></mml:mrow></mml:mfrac></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mrow><mml:mo>}</mml:mo></mml:mrow><mml:mspace width=0.25 /><mml:mo>></mml:mo><mml:mspace width=0.25 /><mml:mi>β</mml:mi></mml:mrow></mml:math> where | δ | < π and cos δ > β . The second Hankel determinant <?CDATA $|{a}_{2}{a}_{4}-{a}_{3}^{2}|$?> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML overflow=scroll><mml:mrow><mml:mo>|</mml:mo><mml:msub><mml:mi>a</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi>a</mml:mi><mml:mn>4</mml:mn></mml:msub><mml:mspace width=0.25 /><mml:mo>−</mml:mo><mml:mspace width=0.25 /><mml:msubsup><mml:mi>a</mml:mi><mml:mn>3</mml:mn><mml:mn>2</mml:mn></mml:msubsup><mml:mo>|</mml:mo></mml:mrow></mml:math> has been determined for <?CDATA ${S}_{sigma }^{* }(beta,delta )$?> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML overflow=scroll><mml:mrow><mml:msubsup><mml:mi>S</mml:mi><mml:mi>σ</mml:mi><mml:mo>*</mml:mo></mml:msubsup><mml:mo stretchy=false>(</mml:mo><mml:mi>β</mml:mi><mml:mo>,</mml:mo><mml:mspace width=0.25 /><mml:mi>δ</mml:mi><mml:mo stretchy=false>)</mml:mo></mml:mrow></mml:math> . In this paper, we also found the coefficients bound for | a 2 |, | a 3 | and | a 4 |." @default.
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- W3155332581 date "2021-03-01" @default.
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- W3155332581 title "Second Hankel determinant for tilted bi-starlike functions of order β" @default.
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