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Subclasses of bi-univalent functions subordinate to gegenbauer polynomials

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Abstract

In the present paper, we introduce three new classes of bi-univalent functions defined by means of Gegenbauer polynomials. For functions in each of these three bi-univalent function classes, we have derived the estimates of the Taylor–Maclaurin coefficients \(\left| a_{2}\right| \) and \(\left| a_{3}\right| \) and Fekete–Szegö functional problems for functions belonging to these new subclasses. A number of new results are shown to follow upon specializing the parameters involved in our main results.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science and Technology, Irbid National University, Irbid, Jordan

    Ala Amourah

  2. Department of Mathematics, Faculty of Ocean Engineering Technology and Informatics, University Malaysia Terengganu, 21030, Kuala Nerus, Terenggunu, Malaysia

    Zabidin Salleh

  3. Department of Mathematics, Faculty of Science, Al Al-Bayt University, Mafraq, Jordan

    B. A. Frasin

  4. Kohat University of Science and Technology, Kohat, Pakistan

    Muhammad Ghaffar Khan

  5. Govt. Degree College Mardan, Mardan, 23200, Pakistan

    Bakhtiar Ahmad

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  1. Ala Amourah
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  2. Zabidin Salleh
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Correspondence to Ala Amourah.

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Amourah, A., Salleh, Z., Frasin, B.A. et al. Subclasses of bi-univalent functions subordinate to gegenbauer polynomials. Afr. Mat. 34, 41 (2023). https://doi.org/10.1007/s13370-023-01082-4

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