Research article

On new subclasses of bi-starlike functions with bounded boundary rotation

  • Received: 14 February 2020 Accepted: 17 March 2020 Published: 30 March 2020
  • MSC : 30C45, 30C50

  • In this paper, we introduce two new classes $\mathcal{B}_{\Sigma}^\lambda(m, \mu)$ of $\lambda$-pseudo bi-starlike functions and $\mathcal{L}_{\Sigma}^\eta(m, \beta)$ to determine the bounds for $|a_2|$ and $|a_3|, $ where $a_2$, $a_3$ are the initial Taylor coefficients of $f\in\mathcal{B}_{\Sigma}^\lambda(m, \mu)$ and $f\in\mathcal{L}_{\Sigma}^\eta(m, \beta).$ Also, we attain the upper bounds of the Fekete-Szegö inequality by means of the results of $|a_2|$ and $|a_3|$.

    Citation: Yumao Li, K. Vijaya, G. Murugusundaramoorthy, Huo Tang. On new subclasses of bi-starlike functions with bounded boundary rotation[J]. AIMS Mathematics, 2020, 5(4): 3346-3356. doi: 10.3934/math.2020215

    Related Papers:

  • In this paper, we introduce two new classes $\mathcal{B}_{\Sigma}^\lambda(m, \mu)$ of $\lambda$-pseudo bi-starlike functions and $\mathcal{L}_{\Sigma}^\eta(m, \beta)$ to determine the bounds for $|a_2|$ and $|a_3|, $ where $a_2$, $a_3$ are the initial Taylor coefficients of $f\in\mathcal{B}_{\Sigma}^\lambda(m, \mu)$ and $f\in\mathcal{L}_{\Sigma}^\eta(m, \beta).$ Also, we attain the upper bounds of the Fekete-Szegö inequality by means of the results of $|a_2|$ and $|a_3|$.


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