Horadam polynomials for a new family of \(\lambda \)-pseudo bi-univalent functions associated with Sakaguchi type functions

Abstract

In the present article, we introduce and study a new family \(\mathcal {F}_{\Sigma }(\delta ,\lambda ,m,n,r)\) of normalized analytic and bi-univalent functions associating \(\lambda \)-pseudo functions with Sakaguchi type functions by using the Horadam polynomials. We obtain upper bounds for the initial Taylor–Maclaurin coefficients \(|a_2|\) and \(|a_3|\). Further we obtain the Fekete–Szegö inequality for functions in the family \(\mathcal {F}_{\Sigma }(\delta ,\lambda ,m,n,r)\) which we have introduced here. We also indicate several certain special cases and consequences for our results.

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The author would like to thank the referee(s) for their helpful comments and suggestions.

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Correspondence to Abbas Kareem Wanas.

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Wanas, A.K. Horadam polynomials for a new family of \(\lambda \)-pseudo bi-univalent functions associated with Sakaguchi type functions. Afr. Mat. (2021). https://doi.org/10.1007/s13370-020-00867-1

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Keywords

  • Analytic functions
  • Univalent functions
  • Bi-univalent functions
  • Horadam polynomials
  • Upper bounds
  • Fekete–Szegö problem
  • Subordination between analytic functions

Mathematics Subject Classification

  • Primary 30C45
  • Secondary 30C50
  • 33C05