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q-Analogue of Differential Subordinations

Author

Listed:
  • Miraj Ul-Haq

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

  • Mohsan Raza

    (Department of Mathematics, Government College University Faisalabad, Faisalabad 38000, Pakistan)

  • Muhammad Arif

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

  • Qaiser Khan

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

  • Huo Tang

    (School of Mathematics and Statistics, Chifeng University, Chifeng 024000, China)

Abstract

In this article, we study differential subordnations in q -analogue. Some properties of analytic functions in q -analogue associated with cardioid domain and limacon domain are considered. In particular, we determine conditions on α such that 1 + α z ∂ q h z h z n ( n = 0 , 1 , 2 , 3 ) are subordinated by Janowski functions and h z ≺ 1 + 4 3 z + 2 3 z 2 . We also consider the same implications such that h z ≺ 1 + 2 z + 1 2 z 2 . We apply these results on analytic functions to find sufficient conditions for q -starlikeness related with cardioid and limacon.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:8:p:724-:d:256310
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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. 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.
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    Cited by:

    1. Ekram Elsayed Ali & Teodor Bulboacă, 2020. "Subclasses of Multivalent Analytic Functions Associated with a q -Difference Operator," Mathematics, MDPI, vol. 8(12), pages 1-8, December.
    2. 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.
    3. 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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