Abstract
In this paper, we establish some applications of first order differential subordination and superordination results involving Hadamard product for a certain class of analytic functions with differential operator defined in the open unit disk. These results are applied to obtain sandwich results.
Highlights
Introduction and PreliminariesLet H indicate the family of analytic functions in the open unit diskU = {z ∈ C : z < 1} and let H[a, p] be the subclass of H consisting of functions of the form:f (z) = a + a p z p + a p+1z p+1 + ⋯, (a ∈ C, p ∈ N = {1, 2, ...}).let A denote the subclass of H consisting of functions of the form: ∑∞f (z) = z + anzn, (1.1) n=2Received: February 22, 2019; Accepted: March 24, 20192010 Mathematics Subject Classification: 30C45.Keywords and phrases: analytic functions, differential subordination, differential superordination, Hadamard product, differential operator
We establish some applications of first order differential subordination and superordination results involving Hadamard product for a certain class of analytic functions with differential operator defined in the open unit disk
U = {z ∈ C : z < 1} and let H[a, p] be the subclass of H consisting of functions of the form: f (z) = a + a p z p + a p+1z p+1 + ⋯, (a ∈ C, p ∈ N = {1, 2, ...})
Summary
U = {z ∈ C : z < 1} and let H[a, p] be the subclass of H consisting of functions of the form:. Let A denote the subclass of H consisting of functions of the form:. Keywords and phrases: analytic functions, differential subordination, differential superordination, Hadamard product, differential operator
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