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Some Janowski Type Harmonic q -Starlike Functions Associated with Symmetrical Points

Author

Listed:
  • Muhammad Arif

    (Faculty of Physical and Numerical Sciences, Abdul Wali Khan University Mardan, Mardan 23200, Pakistan)

  • Omar Barkub

    (Faculty of Computing and Information Technology, King Abdulaziz University, Rabigh 21911, Jeddah, Saudi Arabia)

  • Hari Mohan 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)

  • Saleem Abdullah

    (Faculty of Physical and Numerical Sciences, Abdul Wali Khan University Mardan, Mardan 23200, Pakistan)

  • Sher Afzal Khan

    (Faculty of Physical and Numerical Sciences, Abdul Wali Khan University Mardan, Mardan 23200, Pakistan)

Abstract

The motive behind this article is to apply the notions of q -derivative by introducing some new families of harmonic functions associated with the symmetric circular region. We develop a new criterion for sense preserving and hence the univalency in terms of q -differential operator. The necessary and sufficient conditions are established for univalency for this newly defined class. We also discuss some other interesting properties such as distortion limits, convolution preserving, and convexity conditions. Further, by using sufficient inequality, we establish sharp bounds of the real parts of the ratios of harmonic functions to its sequences of partial sums. Some known consequences of the main results are also obtained by varying the parameters.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:4:p:629-:d:347542
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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. 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.
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    Cited by:

    1. Abdel Moneim Y. Lashin & Fatma Z. El-Emam, 2022. "On Certain Classes of Multivalent Analytic Functions Defined with Higher-Order Derivatives," Mathematics, MDPI, vol. 11(1), pages 1-9, December.
    2. 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.

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