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Hankel and Toeplitz Determinants for a Subclass of q -Starlike Functions Associated with a General Conic Domain

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  • 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)

  • Qazi Zahoor Ahmad

    (Department of Mathematics, Abbottabad University of Science and Technology, Abbottabad 22010, Pakistan)

  • Nasir Khan

    (Department of Mathematics, FATA University, Akhorwal (Darra Adam Khel), FR Kohat 26000, Pakistan)

  • Nazar Khan

    (Department of Mathematics, Abbottabad University of Science and Technology, Abbottabad 22010, Pakistan)

  • Bilal Khan

    (Department of Mathematics, Abbottabad University of Science and Technology, Abbottabad 22010, Pakistan)

Abstract

By using a certain general conic domain as well as the quantum (or q -) calculus, here we define and investigate a new subclass of normalized analytic and starlike functions in the open unit disk U . In particular, we find the Hankel determinant and the Toeplitz matrices for this newly-defined class of analytic q -starlike functions. We also highlight some known consequences of our main results.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:2:p:181-:d:206249
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    References listed on IDEAS

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    1. A. K. Mishra & P. Gochhayat, 2008. "Second Hankel Determinant for a Class of Analytic Functions Defined by Fractional Derivative," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2008, pages 1-10, March.
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    Cited by:

    1. Isra Al-Shbeil & Muhammad Imran Faisal & Muhammad Arif & Muhammad Abbas & Reem K. Alhefthi, 2023. "Investigation of the Hankel Determinant Sharp Bounds for a Specific Analytic Function Linked to a Cardioid-Shaped Domain," Mathematics, MDPI, vol. 11(17), pages 1-22, August.
    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.
    3. Lei Shi & Izaz Ali & Muhammad Arif & Nak Eun Cho & Shehzad Hussain & Hassan Khan, 2019. "A Study of Third Hankel Determinant Problem for Certain Subfamilies of Analytic Functions Involving Cardioid Domain," Mathematics, MDPI, vol. 7(5), pages 1-15, May.
    4. Muhammad Arif & Safa Marwa & Qin Xin & Fairouz Tchier & Muhammad Ayaz & Sarfraz Nawaz Malik, 2022. "Sharp Coefficient Problems of Functions with Bounded Turnings Subordinated by Sigmoid Function," Mathematics, MDPI, vol. 10(20), pages 1-24, October.
    5. Hari Mohan Srivastava & Nazar Khan & Maslina Darus & Shahid Khan & Qazi Zahoor Ahmad & Saqib Hussain, 2020. "Fekete-Szegö Type Problems and Their Applications for a Subclass of q -Starlike Functions with Respect to Symmetrical Points," Mathematics, MDPI, vol. 8(5), pages 1-18, May.
    6. 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.
    7. Huo Tang & Ihtesham Gul & Saqib Hussain & Saima Noor, 2023. "Bounds for Toeplitz Determinants and Related Inequalities for a New Subclass of Analytic Functions," Mathematics, MDPI, vol. 11(18), pages 1-15, September.
    8. Hai-Yan Zhang & Rekha Srivastava & Huo Tang, 2019. "Third-Order Hankel and Toeplitz Determinants for Starlike Functions Connected with the Sine Function," Mathematics, MDPI, vol. 7(5), pages 1-10, May.
    9. 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.
    10. 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.
    11. Hari M. Srivastava & Nazar Khan & Shahid Khan & Qazi Zahoor Ahmad & Bilal Khan, 2021. "A Class of k -Symmetric Harmonic Functions Involving a Certain q -Derivative Operator," Mathematics, MDPI, vol. 9(15), pages 1-14, July.
    12. Loriana Andrei & Vasile-Aurel Caus, 2024. "Subordinations Results on a q -Derivative Differential Operator," Mathematics, MDPI, vol. 12(2), pages 1-20, January.
    13. Hari M. Srivastava & Qazi Zahoor Ahmad & Maslina Darus & Nazar Khan & Bilal Khan & Naveed Zaman & Hasrat Hussain Shah, 2019. "Upper Bound of the Third Hankel Determinant for a Subclass of Close-to-Convex Functions Associated with the Lemniscate of Bernoulli," Mathematics, MDPI, vol. 7(9), pages 1-10, September.
    14. 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.
    15. Shahid Khan & Saqib Hussain & Muhammad Naeem & Maslina Darus & Akhter Rasheed, 2021. "A Subclass of q -Starlike Functions Defined by Using a Symmetric q -Derivative Operator and Related with Generalized Symmetric Conic Domains," Mathematics, MDPI, vol. 9(9), pages 1-12, April.

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