New Applications of Faber Polynomial Expansion for Analytical Bi-Close-to-Convex Functions Defined by Using q -Calculus

Ridong Wang, Manoj Singh, Shahid Khan (), Huo Tang, Mohammad Faisal Khan and Mustafa Kamal
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Ridong Wang: School of Mathematics and Computer Sciences, Chifeng University, Chifeng 024000, China
Manoj Singh: Department of Mathematics, Faculty of Science, Jazan University, Jazan 45142, Saudi Arabia
Shahid Khan: Department of Mathematics, Abbottabad University of Science and Technology, Abbottabad 22500, Pakistan
Huo Tang: School of Mathematics and Computer Sciences, Chifeng University, Chifeng 024000, China
Mohammad Faisal Khan: Department of Basic Science, College of Science and Theoretical Studies, Saudi Electronic University, Riyadh 11673, Saudi Arabia
Mustafa Kamal: Department of Basic Science, College of Science and Theoretical Studies, Saudi Electronic University, Riyadh 11673, Saudi Arabia

Mathematics, 2023, vol. 11, issue 5, 1-15

Abstract: In this investigation, the q -difference operator and the Sălăgean q -differential operator are utilized to establish novel subclasses of analytical bi-close-to-convex functions. We determine the general Taylor–Maclaurin coefficient of the functions in this class using the Faber polynomial method. We demonstrate the unpredictable behaviour of initial coefficients a 2 , a 3 and investigate the Fekete–Szegő problem a 3 − a 2 2 for the subclasses of bi-close-to-convex functions. To highlight the connections between existing knowledge and new research, certain known and unknown corollaries are also highlighted.

Keywords: analytic functions; quantum (or q -) calculus; q -derivative operator; close-to-convex functions; bi-univalent functions; Faber polynomial expansion (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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