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New Families of Bi-univalent Functions Associated with the Bazilevič Functions and the \(\lambda\)-Pseudo-Starlike Functions

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Abstract

In this article, we define two new families \({\mathcal{T}}_{\Sigma }(\mu ,\gamma ,\lambda ;\alpha )\) and \({\mathcal{T}}_{\Sigma }^{*}(\mu ,\gamma ,\lambda ;\beta )\) of normalized holomorphic and bi-univalent functions which involve the Bazilevič functions and the \(\lambda\)-pseudo-starlike functions. For functions in each of these families, we establish the bounds for \(|a_2|\) and \(|a_3|\), where \(a_2\) and \(a_3\) are the initial Taylor-Maclaurin coefficients. We also point out several special cases and consequences of our results.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Victoria, Victoria, BC, V8W 3R4, Canada

    H. M. Srivastava

  2. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, 40402, Taiwan, Republic of China

    H. M. Srivastava

  3. Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, Baku, AZ1007, Azerbaijan

    H. M. Srivastava

  4. Section of Mathematics, International Telematic, University Uninettuno, I-00186, Rome, Italy

    H. M. Srivastava

  5. Department of Mathematics, College of Science, University of Al-Qadisiyah, Al Diwaniyah, Al-Qadisiyah, Iraq

    Abbas Kareem Wanas

  6. Department of Mathematics, Faculty of Science, Dicle University, Diyarbakır, Turkey

    H. Özlem Güney

Authors
  1. H. M. Srivastava
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  2. Abbas Kareem Wanas
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  3. H. Özlem Güney
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Correspondence to Abbas Kareem Wanas.

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Srivastava, H.M., Wanas, A.K. & Güney, H.Ö. New Families of Bi-univalent Functions Associated with the Bazilevič Functions and the \(\lambda\)-Pseudo-Starlike Functions. Iran J Sci Technol Trans Sci 45, 1799–1804 (2021). https://doi.org/10.1007/s40995-021-01176-3

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  • DOI: https://doi.org/10.1007/s40995-021-01176-3

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