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Journals / Bitlis Eren Üniversitesi Fen Bilimleri Dergisi / 2026 / Volume: 13 Issue: 1

On Conic Equations Under Bernstein Operators

Tuncay Tunç(MERSİN ÜNİVERSİTESİ)0000-0002-3061-7197
Ghofran Alhazzori0000-0003-0342-1575
Pages
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Publication Date
2024-03-24
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AI Summary & Key Takeaways

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

In this study, it is investigated whether conic equations transform into a conic equation under bivariate Bernstein polynomials, and if so, which conic equation it transforms into.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:One of the most important problems in approximation theory in mathematical analysis is the determination of sequences of polynomials that converge to functions and have the same geometric properties.
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Key Findings & Data:This type of approximation is called the shape-preserving approximation.
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Conclusion & Impact:In this study, it is investigated whether conic equations transform into a conic equation under bivariate Bernstein polynomials, and if so, which conic equation it transforms into.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Bivariate Bernstein polynomials · Conic equations · Shape-preserving approximation

Abstract

One of the most important problems in approximation theory in mathematical analysis is the determination of sequences of polynomials that converge to functions and have the same geometric properties. This type of approximation is called the shape-preserving approximation. These types of problems are usually handled depending on the convexity of the functions, the degree of smoothness depending on the order of differentiability, or whether it satisfies a functional equation. The problem addressed in this paper belongs to the third class. A quadratic bivariate algebraic equation denotes geometrically some well-known shapes such as circles, ellipses, hyperbolas and parabolas. Such equations are known as conic equations. In this study, it is investigated whether conic equations transform into a conic equation under bivariate Bernstein polynomials, and if so, which conic equation it transforms into.

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Cite This Article

Tunç, T., Alhazzori, G. (2024). On Conic Equations Under Bernstein Operators. Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, Volume: 13 Issue: 1. https://doi.org/10.17798/bitlisfen.1364241

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