Differential subordination and superordination studies involving symmetric functions using a $ q $-analogue multiplier operator

Ekram E. Ali; Georgia Irina Oros; Abeer M. Albalahi; Ekram E. Ali; Georgia Irina Oros; Abeer M. Albalahi

doi:10.3934/math.20231428

AIMS Mathematics

2023, Volume 8, Issue 11: 27924-27946. doi: 10.3934/math.20231428

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Differential subordination and superordination studies involving symmetric functions using a $ q $-analogue multiplier 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 and Computer Science, University of Oradea, Universitatii 1, 410087 Oradea, Romania

Received: 08 July 2023 Revised: 19 September 2023 Accepted: 21 September 2023 Published: 10 October 2023
MSC : 30C45, 30C80

The present investigation focus on applying the theories of differential subordination, differential superordination and related sandwich-type results for the study of some subclasses of symmetric functions connected through a linear extended multiplier operator, which was previously defined by involving the $ q $-Choi-Saigo-Srivastava operator. The aim of the paper is to define a new class of analytic functions using the aforementioned linear extended multiplier operator and to obtain sharp differential subordinations and superordinations using functions from the new class. Certain subclasses are highlighted by specializing the parameters involved in the class definition, and corollaries are obtained as implementations of those new results using particular values for the parameters of the new subclasses. In order to show how the results apply to the functions from the recently introduced subclasses, numerical examples are also provided.
Citation: Ekram E. Ali, Georgia Irina Oros, Abeer M. Albalahi. Differential subordination and superordination studies involving symmetric functions using a $ q $-analogue multiplier operator[J]. AIMS Mathematics, 2023, 8(11): 27924-27946. doi: 10.3934/math.20231428

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Abstract

The present investigation focus on applying the theories of differential subordination, differential superordination and related sandwich-type results for the study of some subclasses of symmetric functions connected through a linear extended multiplier operator, which was previously defined by involving the $ q $-Choi-Saigo-Srivastava operator. The aim of the paper is to define a new class of analytic functions using the aforementioned linear extended multiplier operator and to obtain sharp differential subordinations and superordinations using functions from the new class. Certain subclasses are highlighted by specializing the parameters involved in the class definition, and corollaries are obtained as implementations of those new results using particular values for the parameters of the new subclasses. In order to show how the results apply to the functions from the recently introduced subclasses, numerical examples are also provided.

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