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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 51 Issue: 1

Coefficient inequalities for certain starlike and convex functions

Sushil Kumar Kumar(Bharati Vidyapeeth's College of Engineering)0000-0003-4665-8011
Asena Çetinkaya(ISTANBUL KULTUR UNIVERSITY)0000-0002-8815-5642
Pages
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Publication Date
2022-02-14
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AI Summary & Key Takeaways

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

In addition, we compute best possible estimates on third order Hermitian--Toeplitz determinant and non-sharp estimates on certain third order Hankel determinants for the starlike functions associated with the interior region of Nephroid.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we consider two Ma--Minda-type subclasses of starlike and convex functions associated with the normalized analytic function $\varphi_{Ne}(z)=1+z-z^3/3$ that maps an open unit disk onto the Nephroid shaped bounded domain in the right--half of the complex plane.
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Key Findings & Data:We investigate convolution and quasi-Hadamard product properties for the functions belonging to such classes.
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Conclusion & Impact:In addition, we compute best possible estimates on third order Hermitian--Toeplitz determinant and non-sharp estimates on certain third order Hankel determinants for the starlike functions associated with the interior region of Nephroid.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Starlike functions · convex functions · Neproid

Abstract

In this paper, we consider two Ma--Minda-type subclasses of starlike and convex functions associated with the normalized analytic function $\varphi_{Ne}(z)=1+z-z^3/3$ that maps an open unit disk onto the Nephroid shaped bounded domain in the right--half of the complex plane. We investigate convolution and quasi-Hadamard product properties for the functions belonging to such classes. In addition, we compute best possible estimates on third order Hermitian--Toeplitz determinant and non-sharp estimates on certain third order Hankel determinants for the starlike functions associated with the interior region of Nephroid.

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Cite This Article

Kumar, S. K., Çetinkaya, A. (2022). Coefficient inequalities for certain starlike and convex functions. Hacettepe Journal of Mathematics and Statistics, Volume: 51 Issue: 1. https://doi.org/10.15672/hujms.778148

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