Sharp inequalities for $ q $-starlike functions associated with differential subordination and $ q $-calculus

Jianhua Gong; Muhammad Ghaffar Khan; Hala Alaqad; Bilal Khan; Jianhua Gong; Muhammad Ghaffar Khan; Hala Alaqad; Bilal Khan

doi:10.3934/math.20241379

AIMS Mathematics

2024, Volume 9, Issue 10: 28421-28446. doi: 10.3934/math.20241379

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Sharp inequalities for $ q $-starlike functions associated with differential subordination and $ q $-calculus

1.
Department of Mathematical Sciences, United Arab Emirates University, Al Ain 15551, United Arab Emirates
2.
Institute of Numerical Sciences, Kohat University of Sciences and Technology, Kohat 26000, Pakistan
3.
Institute of Mathematics, Henan Academy of Sciences, Zhengzhou 450046, China

Received: 19 August 2024 Revised: 24 September 2024 Accepted: 27 September 2024 Published: 08 October 2024
MSC : 05A30, 30C45

This paper employs differential subordination and quantum calculus to investigate a new class of $ q $-starlike functions associated with an eight-like image domain. Our study laid a foundational understanding of the behavior of these $ q $-starlike functions. We derived the results in first-order differential subordination. We established sharp inequalities for the initial Taylor coefficients and provided optimal estimates for solving the Fekete-Szegö problem and a second-order Hankel determinant applicable to all $ q $-starlike functions in this class. Furthermore, we presented a series of corollaries that demonstrate the broader implications of our findings in geometric function theory.
- analytic functions,
- univalent functions,
- starlike functions,
- $ q $-starlike functions,
- $ q $-derivative operator,
- differential subordination
Citation: Jianhua Gong, Muhammad Ghaffar Khan, Hala Alaqad, Bilal Khan. Sharp inequalities for $ q $-starlike functions associated with differential subordination and $ q $-calculus[J]. AIMS Mathematics, 2024, 9(10): 28421-28446. doi: 10.3934/math.20241379

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Abstract

This paper employs differential subordination and quantum calculus to investigate a new class of $ q $-starlike functions associated with an eight-like image domain. Our study laid a foundational understanding of the behavior of these $ q $-starlike functions. We derived the results in first-order differential subordination. We established sharp inequalities for the initial Taylor coefficients and provided optimal estimates for solving the Fekete-Szegö problem and a second-order Hankel determinant applicable to all $ q $-starlike functions in this class. Furthermore, we presented a series of corollaries that demonstrate the broader implications of our findings in geometric function theory.

References

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