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Open Access ·Peer-reviewed·ISSN (Online): 2169-012X·ISSN (Print): 0972-0502

Monthly Journal: Publishes the methodological and theoretical role of mathematics and mathematical applications underpinning scientific research.

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Open Access Research Article

Some properties of subordination differential and superordination for univalent functions associated with the convolution operators

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pp. 619–628Vol. 26Issue 4June 2023DOI: 10.47974/JIM-1480XML
Received:
01 Feb 2022
Accepted:
01 Mar 2022
Published Online:
15 Jul 2023
Article type:
Research Article
Language:
EN
Article no.:
JIM-1480
Pages:
619–628

Abstract

In this paper, we define the Hadamard product (or convolution) (f * y([h])) (x)  of the analytic function in the unit disk µ = [ξ : |ξ| < 1, ξ ∈ Ȼ] with the non-zero parameter h, satisfactory to the relationship hη (f * ψ([η]))(ξ) = (hη - 1) (f * ψ([η + 1])) (ξ) + ξ(f * ψ([η + 1]))′ (ξ), to derive  subordination, superordination and sandwich results for functions of the form (f * ψ([η]))(ξ)  by using some properties of Subordination and Superordination concepts. Our results serve to generalize and improve some previous studies where the results of this research were applied to linear operator Bbd  band the multiplier operator ℑiℓ,m. This work can be generalized to other linear operators.

Keywords

Subject Classifications

Primary 93A30Secondary 49K15

References

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