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Sharp Initial Coefficient Bounds and the Fekete–Szegő Problem for Some Subclasses of Analytic and Bi-Univalent Functions

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Ukrainian Mathematical Journal Aims and scope

We introduce two new subclasses UΣ(α, λ) and ℬ1Σ(α) of analytic bi-univalent functions defined in an open unit disk 𝕌, which are associated with the Bazilevich functions. In addition, for functions from these subclasses, we obtain sharp bounds for the initial Taylor–Maclaurin coefficients a2 and a3, as well as the sharp estimate for the Fekete–Szegő functional \({a}_{3}-{\mu a}_{2}^{2}.\)

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Authors and Affiliations

  1. AISSMS College of Engineering, Pune, India

    A. B. Patil

  2. Landmark University, Omu-Aran, Nigeria

    T. G. Shaba

Authors
  1. A. B. Patil
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  2. T. G. Shaba
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Correspondence to A. B. Patil.

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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 74, No. 2, pp. 198–206, February, 2023. Ukrainian https://doi.org/10.37863/umzh.v75i2.6602.

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Patil, A.B., Shaba, T.G. Sharp Initial Coefficient Bounds and the Fekete–Szegő Problem for Some Subclasses of Analytic and Bi-Univalent Functions. Ukr Math J 75, 225–234 (2023). https://doi.org/10.1007/s11253-023-02195-6

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  • DOI: https://doi.org/10.1007/s11253-023-02195-6

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