Certain class of m-fold functions by applying Faber polynomial expansions

Ahmad Motamednezhad, Safa Salehian

Abstract


‎In this paper‎, ‎we introduce new class $\Sigma_{m}(\mu,\lambda,\gamma,\beta)$ of $m$-fold symmetric bi-univalent functions‎. ‎Furthermore‎, ‎we use the Faber polynomial expansions to find upper bounds for the general coefficients $|a_{mk+1}|(k \geqq 2)$ of functions in the class $\Sigma_{m}(\mu,\lambda,\gamma,\beta)$‎. ‎Moreover‎, ‎we obtain estimates for the initial coefficients $|a_{m+1}| $ and $|a_{2m+1}|$ for functions in this class‎. ‎The results presented in this paper would generalize and improve some recent works‎.

Keywords


m-fold symmetric bi-univalent functions‎, ‎Coefficient estimates‎, ‎Faber polynomial expansions

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References


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DOI: http://dx.doi.org/10.24193/subbmath.2021.3.07

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