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Journals / Hacettepe Journal of Mathematics and Statistics / 2021 / Cilt: 50 - Sayı: 3

Some special families of holomorphic and Sălăgean type bi-univalent functions associated with Horadam polynomials involving a modified sigmoid activation function

Sondekola Rudra SWAMY
Serap BULUT
Yerragunta SAILAJA
Pages
710–720
Publication Date
2022-10-18
DOI
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AI Summary & Key Takeaways

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

Some interesting consequences of the results established here are also indicated.

📌 3 Key Takeaways

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Objective & Hypothesis:The aim of this paper is to introduce some special families of holomorphic and S\u{a}l\u{a}gean type bi-univalent functions by making use of Horadam polynomials involving the modified sigmoid activation function $\phi(s)=\frac{2}{1+e^{-s} },\,s\geq0$ in the open unit disc $\mathfrak{D}$.
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Key Findings & Data:We investigate the upper bounds on initial coefficients for functions of the form $g_{\phi}(z)=z+\sum\limits_{j=2}^{\infty}\phi(s)d_jz^j$, in these newly introduced special families and also discuss the Fekete-Szegö problem.
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Conclusion & Impact:Some interesting consequences of the results established here are also indicated.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Holomorphic function · Bi-univalent function · Fekete - Szegö inequality

Abstract

The aim of this paper is to introduce some special families of holomorphic and S\u{a}l\u{a}gean type bi-univalent functions by making use of Horadam polynomials involving the modified sigmoid activation function $\phi(s)=\frac{2}{1+e^{-s} },\,s\geq0$ in the open unit disc $\mathfrak{D}$. We investigate the upper bounds on initial coefficients for functions of the form $g_{\phi}(z)=z+\sum\limits_{j=2}^{\infty}\phi(s)d_jz^j$, in these newly introduced special families and also discuss the Fekete-Szegö problem. Some interesting consequences of the results established here are also indicated.

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Cite This Article

SWAMY, S. R., BULUT, S., SAILAJA, Y. (2022). Some special families of holomorphic and Sălăgean type bi-univalent functions associated with Horadam polynomials involving a modified sigmoid activation function. Hacettepe Journal of Mathematics and Statistics, Cilt: 50 - Sayı: 3, 710–720. https://ajindex.com/articles/529969

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