Starlikeness Condition for a New Differential-Integral Operator

Mugur Acu and Gheorghe Oros
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Mugur Acu: Department of Mathematics and Informatics, Lucian Blaga University of Sibiu, Str. Dr. I. Raţiu, No. 5-7, RO-550012 Sibiu, Romania
Gheorghe Oros: Department of Mathematics, University of Oradea, Str. Universităţii, No.1, 410087 Oradea, Romania

Mathematics, 2020, vol. 8, issue 5, 1-9

Abstract: A new differential-integral operator of the form I n f ( z ) = ( 1 − λ ) S n f ( z ) + λ L n f ( z ) , z ∈ U , f ∈ A , 0 ≤ λ ≤ 1 , n ∈ N is introduced in this paper, where S n is the S?l?gean differential operator and L n is the Alexander integral operator. Using this operator, a new integral operator is defined as: F ( z ) = β + γ z γ ∫ 0 z I n f ( z ) · t β + γ − 2 d t 1 β , where I n f ( z ) is the differential-integral operator given above. Using a differential subordination, we prove that the integral operator F ( z ) is starlike.

Keywords: differential subordination; analytic function; univalent function; convex function; starlike function; dominant; best dominant (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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