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Article

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

1
School of Mathematical Sciences, East China Normal University, 500 Dongchuan Road, Shanghai 200241, China
2
Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada
3
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
4
Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, AZ1007 Baku, Azerbaijan
5
Department of Mathematics, Abbottabad University of Science and Technology, Abbottabad 22010, Pakistan
6
Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi 43600, Selangor, Malaysia
7
Government Akhtar Nawaz Khan (Shaheed) Degree College KTS, Haripur 22620, Pakistan
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(8), 1334; https://doi.org/10.3390/math8081334
Received: 19 May 2020 / Revised: 25 July 2020 / Accepted: 5 August 2020 / Published: 11 August 2020
(This article belongs to the Special Issue New Frontiers in Applied Mathematics and Statistics)
First, by making use of the concept of basic (or q-) calculus, as well as the principle of subordination between analytic functions, generalization Rq(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 H2(1) for functions belonging to this class Rq(h) are investigated. Furthermore, similar results are examined and presented for the functions zf(z) and f1(z). For the validity of our results, relevant connections with those in earlier works are also pointed out. View Full-Text
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 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
MDPI and ACS Style

Khan, B.; Srivastava, H.M.; Khan, N.; Darus, M.; Tahir, M.; Ahmad, Q.Z. Coefficient Estimates for a Subclass of Analytic Functions Associated with a Certain Leaf-Like Domain. Mathematics 2020, 8, 1334. https://doi.org/10.3390/math8081334

AMA Style

Khan B, Srivastava HM, Khan N, Darus M, Tahir M, Ahmad QZ. Coefficient Estimates for a Subclass of Analytic Functions Associated with a Certain Leaf-Like Domain. Mathematics. 2020; 8(8):1334. https://doi.org/10.3390/math8081334

Chicago/Turabian Style

Khan, Bilal; Srivastava, Hari M.; Khan, Nazar; Darus, Maslina; Tahir, Muhammad; Ahmad, Qazi Z. 2020. "Coefficient Estimates for a Subclass of Analytic Functions Associated with a Certain Leaf-Like Domain" Mathematics 8, no. 8: 1334. https://doi.org/10.3390/math8081334

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