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A Study of Multivalent q -starlike Functions Connected with Circular Domain

Author

Listed:
  • Lei Shi

    (School of Mathematics and Statistics, Anyang Normal University, Anyang 455002, China)

  • Qaiser Khan

    (Department of Mathematics, Abdul Wali Khan University Mardan, Mardan 23200, KP, Pakistan)

  • Gautam Srivastava

    (Department of Mathematics and Computer Science, Brandon University, 270 18th Street, Brandon, MB R7A 6A9, Canada
    Research Center for Interneural Computing, China Medical University, Taichung 40402, Taiwan)

  • Jin-Lin Liu

    (Department of Mathematics, Yangzhou University, Yangzhou 225002, China)

  • Muhammad Arif

    (Department of Mathematics, Abdul Wali Khan University Mardan, Mardan 23200, KP, Pakistan)

Abstract

Starlike functions have gained popularity both in literature and in usage over the past decade. In this paper, our aim is to examine some useful problems dealing with q -starlike functions. These include the convolution problem, sufficiency criteria, coefficient estimates, and Fekete–Szegö type inequalities for a new subfamily of analytic and multivalent functions associated with circular domain. In addition, we also define and study a Bernardi integral operator in its q -extension for multivalent functions. Furthermore, we will show that the class defined in this paper, along with the obtained results, generalizes many known works available in the literature.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:8:p:670-:d:252218
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    References listed on IDEAS

    as
    1. 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.
    2. T. M. Seoudy & M. K. Aouf, 2014. "Convolution Properties for Certain Classes of Analytic Functions Defined by -Derivative Operator," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-7, October.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Miraj Ul-Haq & Mohsan Raza & Muhammad Arif & Qaiser Khan & Huo Tang, 2019. "q-Analogue of Differential Subordinations," Mathematics, MDPI, vol. 7(8), pages 1-16, August.
    2. Saeed Islam & Muhammad Ghaffar Khan & Bakhtiar Ahmad & Muhammad Arif & Ronnason Chinram, 2020. "Q -Extension of Starlike Functions Subordinated with a Trigonometric Sine Function," Mathematics, MDPI, vol. 8(10), pages 1-14, October.
    3. Abdullah Alotaibi & Muhammad Arif & Mohammed A. Alghamdi & Shehzad Hussain, 2020. "Starlikness Associated with Cosine Hyperbolic Function," Mathematics, MDPI, vol. 8(7), pages 1-16, July.
    4. 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.
    5. Rabha W. Ibrahim & Rafida M. Elobaid & Suzan J. Obaiys, 2020. "A Class of Quantum Briot–Bouquet Differential Equations with Complex Coefficients," Mathematics, MDPI, vol. 8(5), pages 1-13, May.
    6. 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.
    7. Muhammad Naeem & Saqib Hussain & Shahid Khan & Tahir Mahmood & Maslina Darus & Zahid Shareef, 2020. "Janowski Type q -Convex and q -Close-to-Convex Functions Associated with q -Conic Domain," Mathematics, MDPI, vol. 8(3), pages 1-13, March.
    8. Qaiser Khan & Muhammad Arif & Mohsan Raza & Gautam Srivastava & Huo Tang & Shafiq ur Rehman, 2019. "Some Applications of a New Integral Operator in q -Analog for Multivalent Functions," Mathematics, MDPI, vol. 7(12), pages 1-13, December.
    9. Muhammad Arif & Omar Barkub & Hari Mohan Srivastava & Saleem Abdullah & Sher Afzal Khan, 2020. "Some Janowski Type Harmonic q -Starlike Functions Associated with Symmetrical Points," Mathematics, MDPI, vol. 8(4), pages 1-16, April.

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