Inclusion properties for analytic functions of $ q $-analogue multiplier-Ruscheweyh operator

Ekram E. Ali; Rabha M. El-Ashwah; Abeer M. Albalahi; R. Sidaoui; Abdelkader Moumen; Ekram E. Ali; Rabha M. El-Ashwah; Abeer M. Albalahi; R. Sidaoui; Abdelkader Moumen

doi:10.3934/math.2024330

AIMS Mathematics

2024, Volume 9, Issue 3: 6772-6783. doi: 10.3934/math.2024330

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Inclusion properties for analytic functions of $ q $-analogue multiplier-Ruscheweyh operator

1.
Department of Mathematics, College of Science, University of Ha'il, Ha'il 81451, Saudi Arabia
2.
Department of Mathematics and Computer Science, Faculty of Science, Port Said University, Port Said 42521, Egypt
3.
Department of Mathematics, Faculty of Science, Damietta University, New Damietta 34517, Egypt

Received: 15 September 2023 Revised: 17 January 2023 Accepted: 25 January 2023 Published: 19 February 2024
MSC : 30C45, 30C80

The results of this work have a connection with the geometric function theory and they were obtained using methods based on subordination along with information on $ \mathfrak{q} $-calculus operators. We defined the $ \mathfrak{q} $-analogue of multiplier- Ruscheweyh operator of a certain family of linear operators $ I_{\mathfrak{q}, \mu }^{s}(\lambda, \ell) \mathfrak{f}(\varsigma) \; (s\in \mathbb{N}_{0} = \mathbb{N}\cup \{0\}, \mathbb{ N} = \left\{ 1, 2, 3, ..\right\}; \ell, \lambda, \mu \geq 0, 0 < \mathfrak{q} < 1) $. Our major goal was to build some analytic function subclasses using $ I_{ \mathfrak{q}, \mu }^{s}(\lambda, \ell)\mathfrak{f}(\varsigma) $ and to look into various inclusion relationships that have integral preservation features.
Citation: Ekram E. Ali, Rabha M. El-Ashwah, Abeer M. Albalahi, R. Sidaoui, Abdelkader Moumen. Inclusion properties for analytic functions of $ q $-analogue multiplier-Ruscheweyh operator[J]. AIMS Mathematics, 2024, 9(3): 6772-6783. doi: 10.3934/math.2024330

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Abstract

The results of this work have a connection with the geometric function theory and they were obtained using methods based on subordination along with information on $ \mathfrak{q} $-calculus operators. We defined the $ \mathfrak{q} $-analogue of multiplier- Ruscheweyh operator of a certain family of linear operators $ I_{\mathfrak{q}, \mu }^{s}(\lambda, \ell) \mathfrak{f}(\varsigma) \; (s\in \mathbb{N}_{0} = \mathbb{N}\cup \{0\}, \mathbb{ N} = \left\{ 1, 2, 3, ..\right\}; \ell, \lambda, \mu \geq 0, 0 < \mathfrak{q} < 1) $. Our major goal was to build some analytic function subclasses using $ I_{ \mathfrak{q}, \mu }^{s}(\lambda, \ell)\mathfrak{f}(\varsigma) $ and to look into various inclusion relationships that have integral preservation features.

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