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

Georgia Irina Oros

doi:10.24193/subbmath.2023.2.02

Authors

Georgia Irina Oros University of Oradea

DOI:

https://doi.org/10.24193/subbmath.2023.2.02

Keywords:

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

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.

Author Biography

Georgia Irina Oros, University of Oradea

Department of Mathematics and Computer Science,Associate Professor

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