Coefficient bounds for bi-univalent classes defined by Bazilevič functions and convolution

Abstract

In this paper, we obtain bi-univalent theorems for certain classes defined by convolution and Bazilevič functions with bounded boundary rotation. Also, we will find coefficients bounds for \(\ \left| a_{2}\right| ,\ \left| a_{3}\right| \ \) and \(\ \left| 2a_{2}^{2}h_{2}^{2}-a_{3}h_{3}\right| \ \) for the new classes \({\mathsf {W}} _{\alpha ,b,k,\delta }(f*h)\mathsf {\ }\)and \({\mathsf {M}}_{b,k,\delta }(f*h)\mathsf {.}\)

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Correspondence to S. M. Madian.

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Aouf, M.K., Madian, S.M. Coefficient bounds for bi-univalent classes defined by Bazilevič functions and convolution. Bol. Soc. Mat. Mex. 26, 1045–1062 (2020). https://doi.org/10.1007/s40590-020-00304-0

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Keywords

  • Bi-univalent
  • Bazilevič functions
  • Hadamard product
  • Bounded boundary rotation

Mathematics Subject Classification

  • 30C45