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On a subclass of bi-univalent functions defined by convex combination of order α with the Faber polynomial expansion

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Abstract

In this paper, we define new subclasses of bi-univalent functions involving a differential operator in the open unit disc

$$\Delta = \{ z:z \in \mathbb{C}\,\,\,and\,\,\,\left| z \right| < 1\} .$$

Moreover, we use the Faber polynomial expansion to obtain the bounds of the coefficients for functions belong to the subclasses.

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Authors and Affiliations

  1. Normal College, Chifeng University, Chifeng, 024000, China

    Wurenqiqige & Shu-hai Li

  2. Department of Mathematics, Mongolian National University of Education, Ulaanbaatar, 210646, Mongolia

    Wurenqiqige

  3. Department of Applied Mathematics, Mongolian University of Science and Technology, Ulaanbaatar, 210646, Mongolia

    Tsedenbayar Dashdondog

Authors
  1. Wurenqiqige
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  2. Shu-hai Li
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  3. Tsedenbayar Dashdondog
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Correspondence to Wurenqiqige, Shu-hai Li or Tsedenbayar Dashdondog.

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Wurenqiqige, Li, Sh. & Dashdondog, T. On a subclass of bi-univalent functions defined by convex combination of order α with the Faber polynomial expansion. Appl. Math. J. Chin. Univ. 36, 278–286 (2021). https://doi.org/10.1007/s11766-021-4060-7

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  • DOI: https://doi.org/10.1007/s11766-021-4060-7

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