Sufficient conditions for univalence obtained by using the Ruscheweyh-Bernardi differential-integral operator

Georgia Irina Oros

Abstract


In this paper we introduce the Ruscheweyh-Bernardi differential-integral operator \(T^m:A\to A\) defined by
\[T^m[f](z)=(1-\lambda )R^m [f](z)+\lambda B^m[f](z),\ z\in U,\]
where \(R^m\) is the Ruscheweyh differential operator (Definition 1.3) and \(B^m\) is the Bernardi integral operator (Definition 1.1). By using the operator \(T^m\), the class of univalent functions denoted by \(T^m(\lambda ,\beta )\), \(0\le \lambda \le 1\), \(0\le \beta <1\), is defined and several differential subordinations are studied.


Keywords


analytic function; differential operator; integral operator; convex function; univalent function; dominant; best dominant; differential subordination; Briot-Bouquet differential subordination

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References


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DOI: http://dx.doi.org/10.24193/subbmath.2023.2.02

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