1. Differential subordination results obtained by using a new operator.
- Author
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Szatmari, Eszter and Páll-Szabó, Ágnes Orsolya
- Subjects
CONVEX functions ,DERIVATIVES (Mathematics) ,FRACTIONAL differential equations ,MATHEMATICS theorems ,MATHEMATICS - Abstract
In this paper, is defined the operator D
λ,ν,n α,β : A → A, given by Dλ,ν,n α,β f(z) = (1 - α - β)Rν Dn f(z) + αRν Ωλ z f(z) + βDnΩλzf(z), for z ∈ U, where Rν is the Ruscheweyh derivative, Dn is the Sălăgean operator, Ωλ z is a fractional differintegral operator introduced by S. Owa and H. M. Srivastava, A = {f ∈ H(U) : f(z) = z + a2 z² + a3 z³ + ..., z ∈ U}, α, β ≥ 0, ν > -1, n ∈ N0 = {0, 1, 2, 3, ...}, -∞ < λ < 2. A certain subclass of analytic functions in the open unit disk, Rλ,ν,n α,β (δ), where 0 ≤ δ ≤ 1, is introduced using the new operator. Are obtained some properties of the class Rλ,ν,n α,β (δ) and some differential subordinations using the operator Dλ,ν,n α,β . [ABSTRACT FROM AUTHOR]- Published
- 2017