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

A new subclass of analytic functions

Janusz Sokół
Hesam Mahzoon
Pages
1346–1354
Publication Date
2022-10-18
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

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.

📌 3 Key Takeaways

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Objective & Hypothesis: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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Key Findings & Data:Integral representation, differential subordination results and coefficient estimates are considered.
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Conclusion & Impact: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.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables: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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Cite This Article

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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