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Distortions properties of alpha-starlike functions

Distortions properties of alpha-starlike functions

Let <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="alpha"> <mml:semantics> <mml:mi>α<!-- α --></mml:mi> <mml:annotation encoding="application/x-tex">\alpha</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be real and suppose that <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="f left-parenthesis z right-parenthesis equals z plus normal upper Sigma 2 Superscript normal infinity Baseline a Subscript n Baseline z Superscript n"> <mml:semantics> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo …