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A Study on q -Starlike Functions Connected with q -Extension of Hyperbolic Secant and Janowski Functions

Author

Listed:
  • Pengfei Bai

    (School of Mathematics and Computer Sciences, Chifeng University, Chifeng 024000, China)

  • Adeel Ahmad

    (Department of Mathematics and Statistics, Hazara University Mansehra, Dhodial 21120, Pakistan)

  • Akhter Rasheed

    (Department of Mathematics, COMSATS University Islamabad, Abbottabad Campus, Abbottabad 22060, Pakistan)

  • Saqib Hussain

    (Department of Mathematics, COMSATS University Islamabad, Abbottabad Campus, Abbottabad 22060, Pakistan)

  • Huo Tang

    (School of Mathematics and Computer Sciences, Chifeng University, Chifeng 024000, China)

  • Saima Noor

    (Department of Mathematics and Statistics, College of Science, King Faisal University, P.O. Box 400, Al Ahsa 31982, Saudi Arabia
    Department of Basic Sciences, General Administration of Preparatory Year, King Faisal University, P.O. Box 400, Al Ahsa 31982, Saudi Arabia)

Abstract

This study introduces a novel subclass of q -starlike functions that is defined by the application of the q -difference operator and q -analogue of hyperbolic secant function. By making certain variations to the parameter “ q ”, the geometric interpretation of the domain hyperbolic secant function has also been discussed. The primary objective is to investigate and establish key results on the differential subordination of various orders within this newly defined class. Furthermore, convolution properties are explored and coefficient bounds are derived for these functions. A deeper analysis of these coefficients bounds unveils intriguing geometric insights and significant mathematical problems.

Suggested Citation

  • Pengfei Bai & Adeel Ahmad & Akhter Rasheed & Saqib Hussain & Huo Tang & Saima Noor, 2025. "A Study on q -Starlike Functions Connected with q -Extension of Hyperbolic Secant and Janowski Functions," Mathematics, MDPI, vol. 13(13), pages 1-17, July.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:13:p:2173-:d:1693900
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    References listed on IDEAS

    as
    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. Mehwish Jabeen & Sarfraz Nawaz Malik & Shahid Mahmood & S. M. Jawwad Riaz & Md. Shajib Ali & Fairouz Tchier, 2022. "On q-Convex Functions Defined by the q-Ruscheweyh Derivative Operator in Conic Regions," Journal of Mathematics, Hindawi, vol. 2022, pages 1-13, February.
    3. T. N. Shanmugam, 1989. "Convolution and differential subordination," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 12, pages 1-8, January.
    Full references (including those not matched with items on IDEAS)

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