Certain class of m-fold functions by applying Faber polynomial expansions (original) (raw)

Studia Universitatis Babes-Bolyai Matematica

Abstract

"In this paper, we introduce new class Sigmam(mu,lambda,gamma,beta)\Sigma_{m}(\mu,\lambda,\gamma,\beta)Sigmam(mu,lambda,gamma,beta) of mmm-fold symmetric bi-univalent functions. Furthermore, we use the Faber polynomial expansions to find upper bounds for the general coefficients ∣amk+1∣(kgeqq2)|a_{mk+1}|(k \geqq 2)∣amk+1∣(kgeqq2) of functions in the class Sigmam(mu,lambda,gamma,beta)\Sigma_{m}(\mu,\lambda,\gamma,\beta)Sigmam(mu,lambda,gamma,beta). Moreover, we obtain estimates for the initial coefficients ∣am+1∣|a_{m+1}| ∣am+1∣ and ∣a2m+1∣|a_{2m+1}|∣a2m+1∣ for functions in this class. The results presented in this paper would generalize and improve some recent works."

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