New Applications of the Bernardi Integral Operator

Shigeyoshi Owa and H. Özlem Güney
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Shigeyoshi Owa: “1 Decembrie 1918” University Alba Iulia, 510009 Alba-Iulia, Romania
H. Özlem Güney: Department of Mathematics, Faculty of Science Dicle University, 21280 Diyarbakır, Turkey

Mathematics, 2020, vol. 8, issue 7, 1-12

Abstract: Let A ( p , n ) be the class of f ( z ) which are analytic p -valent functions in the closed unit disk U ¯ = z ∈ C : z ≤ 1 . The expression B − m − λ f ( z ) is defined by using fractional integrals of order λ for f ( z ) ∈ A ( p , n ) . When m = 1 and λ = 0 , B − 1 f ( z ) becomes Bernardi integral operator. Using the fractional integral B − m − λ f ( z ) , the subclass T p , n α s , β , ρ ; m , λ of A ( p , n ) is introduced. In the present paper, we discuss some interesting properties for f ( z ) concerning with the class T p , n α s , β , ρ ; m , λ . Also, some interesting examples for our results will be considered.

Keywords: analytic p -valent function; Bernardi integral operator; Libera integral operator; fractional integral; gamma function; Miller–Mocanu lemma (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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