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A Study of Some Families of Multivalent q -Starlike Functions Involving Higher-Order q -Derivatives

Author

Listed:
  • Bilal Khan

    (School of Mathematical Sciences, East China Normal University, 500 Dongchuan Road, Shanghai 200241, China)

  • Zhi-Guo Liu

    (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, Baku AZ1007, 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)

Abstract

In the present investigation, by using certain higher-order q -derivatives, the authors introduce and investigate several new subclasses of the family of multivalent q -starlike functions in the open unit disk. For each of these newly-defined function classes, several interesting properties and characteristics are systematically derived. These properties and characteristics include (for example) distortion theorems and radius problems. A number of coefficient inequalities and a sufficient condition for functions belonging to the subclasses studied here are also discussed. Relevant connections of the various results presented in this investigation with those in earlier works on this subject are also pointed out.

Suggested Citation

  • Bilal Khan & Zhi-Guo Liu & Hari M. Srivastava & Nazar Khan & Maslina Darus & Muhammad Tahir, 2020. "A Study of Some Families of Multivalent q -Starlike Functions Involving Higher-Order q -Derivatives," Mathematics, MDPI, vol. 8(9), pages 1-12, September.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:9:p:1470-:d:407067
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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.
    2. Ben Wongsaijai & Nattakorn Sukantamala, 2016. "Certain Properties of Some Families of Generalized Starlike Functions with respect to -Calculus," Abstract and Applied Analysis, Hindawi, vol. 2016, pages 1-8, September.
    3. Hari M. Srivastava & Qazi Zahoor Ahmad & Nasir Khan & Nazar Khan & Bilal Khan, 2019. "Hankel and Toeplitz Determinants for a Subclass of q -Starlike Functions Associated with a General Conic Domain," Mathematics, MDPI, vol. 7(2), pages 1-15, February.
    Full references (including those not matched with items on IDEAS)

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