Coefficient Estimates for a Subclass of Analytic Functions Associated with a Certain Leaf-Like Domain

Bilal Khan, Hari M. Srivastava, Nazar Khan, Maslina Darus, Muhammad Tahir and Qazi Zahoor Ahmad
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Bilal Khan: School of Mathematical Sciences, East China Normal University, 500 Dongchuan Road, Shanghai 200241, China
Hari M. Srivastava: Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada
Nazar Khan: Department of Mathematics, Abbottabad University of Science and Technology, Abbottabad 22010, Pakistan
Maslina Darus: Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi 43600, Selangor, Malaysia
Muhammad Tahir: Department of Mathematics, Abbottabad University of Science and Technology, Abbottabad 22010, Pakistan
Qazi Zahoor Ahmad: Government Akhtar Nawaz Khan (Shaheed) Degree College KTS, Haripur 22620, Pakistan

Mathematics, 2020, vol. 8, issue 8, 1-15

Abstract: First, by making use of the concept of basic (or q -) calculus, as well as the principle of subordination between analytic functions, generalization R q ( h ) of the class R ( h ) of analytic functions, which are associated with the leaf-like domain in the open unit disk U , is given. Then, the coefficient estimates, the Fekete–Szegö problem, and the second-order Hankel determinant H 2 ( 1 ) for functions belonging to this class R q ( h ) are investigated. Furthermore, similar results are examined and presented for the functions z f ( z ) and f − 1 ( z ) . For the validity of our results, relevant connections with those in earlier works are also pointed out.

Keywords: analytic functions; univalent functions; bounded turning functions; q -derivative (or q -difference) operator; principle of subordination between analytic functions; leaf-like domain; coefficient estimates; Taylor–Maclaurin coefficients; Fekete–Szegö problem; Hankel determinant (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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