New Developments in Geometric Function Theory

Oros, Georgia Irina

doi:10.3390/axioms12010059

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2023

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“…This theory subsequently became very popular and its development was broad and fast. Important contributions to this theory can be found in older papers like [5] and newer publications like [13], [18], [4], [14] and [15].…”

Section: Introductionmentioning

confidence: 99%

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

Oros

2023

Stud. Univ. Babes-Bolyai Math.

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"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 \ref{d1.2}) and $B^m$ is the Bernardi integral operator (Definition \ref{d1.1}). 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."

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