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.
Bivariate Bernstein polynomials Conic equations Shape-preserving approximation Korovkin type theorem.
Primary Language | English |
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Subjects | Approximation Theory and Asymptotic Methods |
Journal Section | Araştırma Makalesi |
Authors | |
Early Pub Date | March 21, 2024 |
Publication Date | March 24, 2024 |
Submission Date | September 21, 2023 |
Acceptance Date | January 22, 2024 |
Published in Issue | Year 2024 Volume: 13 Issue: 1 |