Subclasses of \(\lambda\)-bi-pseudo-starlike functions with respect to symmetric points based on shell-like curves

H. Özlem Güney; G. Murugusundaramoorthy; K. Vijaya

doi:10.4067/S0719-06462021000200299

DOI:

https://doi.org/10.4067/S0719-06462021000200299

Abstract

In this paper we define the subclass \(\mathcal{PSL}^\lambda_{s,\Sigma}(\alpha,\tilde{p}(z))\) of the class \(\Sigma\) of bi-univalent functions defined in the unit disk, called \(\lambda\)-bi-pseudo-starlike, with respect to symmetric points, related to shell-like curves connected with Fibonacci numbers. We determine the initial Taylor-Maclaurin coefficients \(|a_2|\) and \(|a_3|\) for functions \(f\in\mathcal{PSL}^\lambda_{s,\Sigma}(\alpha,\tilde{p}(z)).\) Further we determine the Fekete-Szegö result for the function class \(\mathcal{PSL}^\lambda_{s,\Sigma}(\alpha,\tilde{p}(z))\) and for the special cases \(\alpha=0\), \(\alpha=1\) and \(\tau =-0.618\) we state corollaries improving the initial Taylor-Maclaurin coefficients \(|a_2|\) and \(|a_3|\).

Keywords

Analytic functions , bi-univalent , shell-like curve , Fibonacci numbers , starlike functions

H. Özlem Güney Dicle University, Faculty of Science, Department of Mathematics, DiyarbakÄ±r, Turkey.
G. Murugusundaramoorthy School of Advanced Sciences, Vellore Institute of Technology, Vellore -632014, India.
K. Vijaya School of Advanced Sciences, Vellore Institute of Technology, Vellore -632014, India.

Pages: 299–312
Date Published: 2021-08-01
Vol. 23 No. 2 (2021)

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