IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i13p2857-d1179436.html
   My bibliography  Save this article

Initial Coefficient Bounds for Bi-Univalent Functions Related to Gregory Coefficients

Author

Listed:
  • Gangadharan Murugusundaramoorthy

    (Department of Mathematics, Vellore Institute of Technology (VIT), Vellore 632014, TN, India
    These authors contributed equally to this work.)

  • Kaliappan Vijaya

    (Department of Mathematics, Vellore Institute of Technology (VIT), Vellore 632014, TN, India
    These authors contributed equally to this work.)

  • Teodor Bulboacă

    (Faculty of Mathematics and Computer Science, Babeş-Bolyai University, 400084 Cluj-Napoca, Romania
    These authors contributed equally to this work.)

Abstract

In this article we introduce three new subclasses of the class of bi-univalent functions Σ , namely HG Σ , GM Σ ( μ ) and G Σ ( λ ) , by using the subordinations with the functions whose coefficients are Gregory numbers. First, we evidence that these classes are not empty, i.e., they contain other functions besides the identity one. For functions in each of these three bi-univalent function classes, we investigate the estimates a 2 and a 3 of the Taylor–Maclaurin coefficients and Fekete–Szegő functional problems. The main results are followed by some particular cases, and the novelty of the characterizations and the proofs may lead to further studies of such types of similarly defined subclasses of analytic bi-univalent functions.

Suggested Citation

  • Gangadharan Murugusundaramoorthy & Kaliappan Vijaya & Teodor Bulboacă, 2023. "Initial Coefficient Bounds for Bi-Univalent Functions Related to Gregory Coefficients," Mathematics, MDPI, vol. 11(13), pages 1-16, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:13:p:2857-:d:1179436
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/13/2857/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/13/2857/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Paweł Zaprawa, 2014. "Estimates of Initial Coefficients for Bi-Univalent Functions," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-6, May.
    2. G. Murugusundaramoorthy & N. Magesh & V. Prameela, 2013. "Coefficient Bounds for Certain Subclasses of Bi-Univalent Function," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-3, June.
    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. Rayaprolu Bharavi Sharma & Kalikota Rajya Laxmi, 2016. "Coefficient Inequalities of Second Hankel Determinants for Some Classes of Bi-Univalent Functions," Mathematics, MDPI, vol. 4(1), pages 1-11, February.
    2. Abdulmtalb Hussen & Abdelbaset Zeyani, 2023. "Coefficients and Fekete–Szegö Functional Estimations of Bi-Univalent Subclasses Based on Gegenbauer Polynomials," Mathematics, MDPI, vol. 11(13), pages 1-10, June.
    3. Ibtisam Aldawish & Tariq Al-Hawary & B. A. Frasin, 2020. "Subclasses of Bi-Univalent Functions Defined by Frasin Differential Operator," Mathematics, MDPI, vol. 8(5), pages 1-11, May.
    4. Nizami Mustafa, 2019. "On The Upper Bound Estimates for the Coefficients of Certain Class Bi-Univalent Functions of Complex Order," Academic Journal of Applied Mathematical Sciences, Academic Research Publishing Group, vol. 5(7), pages 101-113, 07-2019.
    5. Şahsene Altınkaya & Sibel Yalçın, 2015. "Coefficient Bounds for Certain Subclasses of -Fold Symmetric Biunivalent Functions," Journal of Mathematics, Hindawi, vol. 2015, pages 1-5, November.
    6. Abdullah Alsoboh & Ala Amourah & Maslina Darus & Rami Issa Al Sharefeen, 2023. "Applications of Neutrosophic q -Poisson distribution Series for Subclass of Analytic Functions and Bi-Univalent Functions," Mathematics, MDPI, vol. 11(4), pages 1-10, February.
    7. Lin-Lin Fan & Zhi-Gang Wang & Shahid Khan & Saqib Hussain & Muhammad Naeem & Tahir Mahmood, 2019. "Coefficient Bounds for Certain Subclasses of q -Starlike Functions," Mathematics, MDPI, vol. 7(10), pages 1-11, October.

    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:11:y:2023:i:13:p:2857-:d:1179436. 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.