By using the Ruscheweyh operator <mml:math alttext="$D^{m}f(z)$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>D</mml:mi><mml:mi>m</mml:mi></mml:msup><mml:mi>f</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>, <mml:math alttext="$z\in U$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>z</mml:mi><mml:mo>&#8712;</mml:mo><mml:mi>U</mml:mi></mml:math>, we will introduce a class of holomorphic functions, denoted by
<mml:math alttext="$M_{n}^{m}(\alpha )$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mi>M</mml:mi><mml:mi>n</mml:mi><mml:mi>m</mml:mi></mml:msubsup><mml:mrow><mml:mo>(</mml:mo><mml:mi>&#945;</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>, and obtain some inclusion relations.

International Journal of Mathematics and Mathematical Sciences

On a class of holomorphic functions defined by the Ruscheweyh derivative

Abstract

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