IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i9p917-d540081.html
   My bibliography  Save this article

A Subclass of q -Starlike Functions Defined by Using a Symmetric q -Derivative Operator and Related with Generalized Symmetric Conic Domains

Author

Listed:
  • Shahid Khan

    (Department of Mathematics, Riphah International University, Islamabad 44000, Pakistan)

  • Saqib Hussain

    (Department of Mathematics, COMSATS University Islamabad, Abbottabad Campus, Abbottabad 22010, Pakistan)

  • Muhammad Naeem

    (Department of Mathematics and Statistic, International Islamic University, Islamabad 44000, Pakistan)

  • Maslina Darus

    (Department of Mathematical Science, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi 43600, Malaysia)

  • Akhter Rasheed

    (Department of Mathematics, COMSATS University Islamabad, Abbottabad Campus, Abbottabad 22010, Pakistan)

Abstract

In this paper, the concepts of symmetric q -calculus and conic regions are used to define a new domain Ω k , q , α ˜ , which generalizes the symmetric conic domains. By using the domain Ω k , q , α ˜ , we define a new subclass of analytic and q -starlike functions in the open unit disk U and establish some new results for functions of this class. We also investigate a number of useful properties and characteristics of this subclass, such as coefficients estimates, structural formulas, distortion inequalities, necessary and sufficient conditions, closure and subordination results. The proposed approach is also compared with some existing methods to show the reliability and effectiveness of the proposed methods.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:9:p:917-:d:540081
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/9/917/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/9/917/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Saeid Shams & S. R. Kulkarni & Jay M. Jahangiri, 2004. "Classes of uniformly starlike and convex functions," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2004, pages 1-3, January.
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. H. Özlem Güney & Serap Bulut, 2013. "Convexity and Spirallikeness Conditions for Two New General Integral Operators," Journal of Mathematics, Hindawi, vol. 2013, pages 1-8, May.
    2. R. M. El-Ashwah & M. K. Aouf & A. A. M. Hassan & A. H. Hassan, 2013. "Subclass of Multivalent -Uniformly Functions with Varying Arguments," Journal of Mathematics, Hindawi, vol. 2013, pages 1-6, January.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. Muhammad Naeem & Saqib Hussain & Tahir Mahmood & Shahid Khan & Maslina Darus, 2019. "A New Subclass of Analytic Functions Defined by Using Salagean q -Differential Operator," Mathematics, MDPI, vol. 7(5), pages 1-13, May.
    9. 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.
    10. Hari M. Srivastava & Nazar Khan & Maslina Darus & Muhammad Tariq Rahim & Qazi Zahoor Ahmad & Yousra Zeb, 2019. "Properties of Spiral-Like Close-to-Convex Functions Associated with Conic Domains," Mathematics, MDPI, vol. 7(8), pages 1-12, August.
    11. Ekram E. Ali & Hari M. Srivastava & Abeer M. Albalahi, 2023. "Subclasses of p -Valent κ -Uniformly Convex and Starlike Functions Defined by the q -Derivative Operator," Mathematics, MDPI, vol. 11(11), pages 1-19, June.
    12. 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.
    13. R. M. El-Ashwah & M. K. Aouf & A. A. M. Hassan & A. H. Hassan, 2013. "A New Class of Analytic Functions Defined by Using Salagean Operator," International Journal of Analysis, Hindawi, vol. 2013, pages 1-10, February.
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    18. 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.
    19. Loriana Andrei & Vasile-Aurel Caus, 2024. "Subordinations Results on a q -Derivative Differential Operator," Mathematics, MDPI, vol. 12(2), pages 1-20, January.
    20. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:9:y:2021:i:9:p:917-:d:540081. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.