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

Author

Listed:
  • 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
    Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
    Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, AZ1007 Baku, Azerbaijan)

  • 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)

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.

Suggested Citation

  • Bilal Khan & Hari M. Srivastava & Nazar Khan & Maslina Darus & Muhammad Tahir & Qazi Zahoor Ahmad, 2020. "Coefficient Estimates for a Subclass of Analytic Functions Associated with a Certain Leaf-Like Domain," Mathematics, MDPI, vol. 8(8), pages 1-15, August.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:8:p:1334-:d:397209
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    References listed on IDEAS

    as
    1. Lei Shi & Qaiser Khan & Gautam Srivastava & Jin-Lin Liu & Muhammad Arif, 2019. "A Study of Multivalent q -starlike Functions Connected with Circular Domain," Mathematics, MDPI, vol. 7(8), pages 1-12, July.
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