Some properties of subordination differential and superordination for univalent functions associated with the convolution operators
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 deriv...
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| Published in: | Journal of interdisciplinary mathematics Vol. 26; no. 4; pp. 619 - 628 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
2023
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| Online Access: | Get full text |
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| Summary: | 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. |
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| ISSN: | 0972-0502 2169-012X |
| DOI: | 10.47974/JIM-1480 |