Coefficient estimates for $m$-fold symmetric bi-subordinate functions

Amaç & Hipotez:A function is said to be bi-univalent in the open unit disk $\mathbb{U}$ if both the function and its inverse map are univalent in $\mathbb{U}$.

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Temel Bulgular & Veri:In this paper, we consider the m-fold symmtric transform of such functions and use their Faber polynomial expansions to find upper bounds for their n-th ($n\geq 3$) coefficients subject to a given gap series condition.

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Sonuç & Katkı:We also determine bounds for the first two coefficients of such functions with no restrictions imposed.

🔬Tür:Research Article

📍Kapsam:Genişletilmiş Akademik Örneklem

⚙️Değişkenler:Faber polynomials · $m$-fold symmetric · bi-univalent functions

Abstract

A function is said to be bi-univalent in the open unit disk $\mathbb{U}$ if both the function and its inverse map are univalent in $\mathbb{U}$. By the same token, a function is said to be bi-subordinate in $\mathbb{U}$ if both the function and its inverse map are subordinate to a given function in $\mathbb{U}$. In this paper, we consider the m-fold symmtric transform of such functions and use their Faber polynomial expansions to find upper bounds for their n-th ($n\geq 3$) coefficients subject to a given gap series condition. We also determine bounds for the first two coefficients of such functions with no restrictions imposed.

Anahtar kelimeler

Faber polynomials $m$-fold symmetric bi-univalent functions

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Bu Makaleye Atıf Yap

Adegani, E. A., Hamidi, S. G., Jahangiri, J. M., Zireh, A. (2019). Coefficient estimates for $m$-fold symmetric bi-subordinate functions. Hacettepe Journal of Mathematics and Statistics, Volume: 48 Issue: 2. https://doi.org/10.15672/hujms.545237

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Kaynakça (12)

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