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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2020 / Cilt: 49 - Sayı: 4

A new subclass of analytic functions

Janusz Sokół
Hesam Mahzoon
Sayfa
1346–1354
Yayın Tarihi
2022-10-18
DOI
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Also Fekete-Szegö coefficient functional associated with the $k$--th root transform $[f(z^k)]^{1/k}$ for functions in the class $\mathcal{B}_\theta(\alpha,\beta)$ is investigated.

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Amaç & Hipotez:In the present paper, we introduce a class $\mathcal{B}_\theta(\alpha,\beta)$ of functions, analytic in $|z|<1$, such that $f(0)=0$, $f'(0)=1$ and\[\alpha< Re\left(f'(z)+\frac{1+e^{i\theta}}{2}zf''(z)\right)<\beta\quad (|z|<1),\]where $\theta\in(-\pi,\pi]$, $0\leq\alpha<1$ and $\beta>1$.
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Temel Bulgular & Veri:Integral representation, differential subordination results and coefficient estimates are considered.
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Sonuç & Katkı:Also Fekete-Szegö coefficient functional associated with the $k$--th root transform $[f(z^k)]^{1/k}$ for functions in the class $\mathcal{B}_\theta(\alpha,\beta)$ is investigated.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:analytic functions · univalent functions · Carathéodory functions

Abstract

In the present paper, we introduce a class $\mathcal{B}_\theta(\alpha,\beta)$ of functions, analytic in $|z|<1$, such that $f(0)=0$, $f'(0)=1$ and\[\alpha< Re\left(f'(z)+\frac{1+e^{i\theta}}{2}zf''(z)\right)<\beta\quad (|z|<1),\]where $\theta\in(-\pi,\pi]$, $0\leq\alpha<1$ and $\beta>1$. Integral representation, differential subordination results and coefficient estimates are considered. Also Fekete-Szegö coefficient functional associated with the $k$--th root transform $[f(z^k)]^{1/k}$ for functions in the class $\mathcal{B}_\theta(\alpha,\beta)$ is investigated.

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Bu Makaleye Atıf Yap

Sokół, J., Mahzoon, H. (2022). A new subclass of analytic functions. Hacettepe Journal of Mathematics and Statistics, Cilt: 49 - Sayı: 4, 1346–1354. https://ajindex.com/articles/529658

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Kaynakça (14)

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