Third Hankel determinant for \(q\)-analogue of symmetric starlike connected to \(q\)-exponential function

Volume 16, Issue 4, pp 198--207 http://dx.doi.org/10.22436/jnsa.016.04.01

Publication Date: October 26, 2023 Submission Date: July 31, 2023 Revision Date: August 23, 2023 Accteptance Date: September 12, 2023

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Authors

Y. Hamayun - Government Post Graduate College Dargai, Pakistan. N. Ullah - Government Post Graduate College Dargai, Pakistan. R. Khan - Government Post Graduate College Dargai, Pakistan. Kh. Ahmad - Government Post Graduate College Dargai, Pakistan. M. Gh. Khan - Institute of Numerical Sciences, Kohat university of science and technology, Kohat, Pakistan. B. Khan - School of Mathematical Sciences and Shanghai Key Laboratory of PMMP, East China Normal University, 500 Dongchuan Road, Shanghai 200241, Peoples Republic of China.

Abstract

By making use of the concept of basic (or \(q\)-) calculus, a subclass of \(q\) -starlike functions with reference to symmetric points, which is associated with the \(q\)-exponential function, is introduced in the open unit disc. Further, we derived upper bounds for the third-order Hankel determinant for the defined class. For the validity of our results, relevant connections with those in earlier works are also pointed out.

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Keywords

• Analytic function
• subordination
• differential operator
• exponential function
• Fekete-Szego functional problems

MSC

•  30C45
•  30C50
•  30C80

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