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Convolution conditions for bounded \(\alpha\)-starlike functions of complex order

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Lashin A. Y.

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

2017

tom 71

nr 1

Let \(A\) be the class of analytic functions in the unit disc \(U\) of the complex plane \(\mathbb{C}\) with the normalization \(f(0)=f^{^{\prime }}(0)-1=0\). We introduce a subclass \(S_{M}^{\ast }(\alpha ,b)\) of \(A\), which unifies the classes of bounded starlike and convex functions of complex order. Making use of Salagean operator, a more general class \(S_{M}^{\ast }(n,\alpha ,b)\) (\(n\geq 0\)) related to \(S_{M}^{\ast }(\alpha ,b)\) is also considered under the same conditions. Among other things, we find convolution conditions for a function \(f\in A\) to belong to the class \(S_{M}^{\ast }(\alpha ,b)\). Several properties of the class \(S_{M}^{\ast }(n,\alpha ,b)\) are investigated.

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1 Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

1 Lashin A. Y.

1 2017

Wyniki wyszukiwania

Convolution conditions for bounded \(\alpha\)-starlike functions of complex order