Some new applications of the quantum-difference operator on subclasses of multivalent $ q $-starlike and $ q $-convex functions associated with the Cardioid domain

Mohammad Faisal Khan; Ahmad A. Abubaker; Suha B. Al-Shaikh; Khaled Matarneh; Mohammad Faisal Khan; Ahmad A. Abubaker; Suha B. Al-Shaikh; Khaled Matarneh

doi:10.3934/math.20231083

AIMS Mathematics

2023, Volume 8, Issue 9: 21246-21269. doi: 10.3934/math.20231083

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Research article

Some new applications of the quantum-difference operator on subclasses of multivalent $ q $-starlike and $ q $-convex functions associated with the Cardioid domain

1.
Department of Basic sciences, College of Science and Theoretical Studies, Saudi Electronic University, Riyadh 11673, Saudi Arabia; f.khan@seu.edu.sa
2.
Faculty of Computer Studies, Arab Open University, Saudi Arabia; a.abubaker@arabou.edu.sa; k.matarneh@arabou.edu.sa

Received: 19 April 2023 Revised: 11 June 2023 Accepted: 18 June 2023 Published: 03 July 2023
MSC : 05A30, 11B65, 30C45, 47B38

In this study, we consider the quantum difference operator to define new subclasses of multivalent $ q $-starlike and $ q $-convex functions associated with the cardioid domain. We investigate a number of interesting problems for functions that belong to these newly defined classes, such as bounds for the first two Taylor-Maclaurin coefficients, estimates for the Fekete-Szeg ö type functional, and coefficient inequalities. The important point of this article is that all the bounds that we have investigated are sharp. Many well-known corollaries are also presented to demonstrate the relationship between prior studies and the results of this article.
- analytic functions,
- univalent functions,
- quantum difference operator,
- $ q $-starlike functions and $ q $-convex functions,
- Fibonacci numbers,
- multivalent functions,
- cardioid domain
Citation: Mohammad Faisal Khan, Ahmad A. Abubaker, Suha B. Al-Shaikh, Khaled Matarneh. Some new applications of the quantum-difference operator on subclasses of multivalent $ q $-starlike and $ q $-convex functions associated with the Cardioid domain[J]. AIMS Mathematics, 2023, 8(9): 21246-21269. doi: 10.3934/math.20231083

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Abstract

In this study, we consider the quantum difference operator to define new subclasses of multivalent $ q $-starlike and $ q $-convex functions associated with the cardioid domain. We investigate a number of interesting problems for functions that belong to these newly defined classes, such as bounds for the first two Taylor-Maclaurin coefficients, estimates for the Fekete-Szeg ö type functional, and coefficient inequalities. The important point of this article is that all the bounds that we have investigated are sharp. Many well-known corollaries are also presented to demonstrate the relationship between prior studies and the results of this article.

References

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