Results 31 to 40 of about 80 (74)

The Peetre K-Functional and the Riesz Summability Operator for the Fourier–Legendre Expansions

Journal of Approximation Theory, 1999
This is an interesting paper, the author extending previous work of Z. Ditzian. It is showed that the Peetre \(K\)-functional and the Riesz operators (a generalized version of of the classical Riesz operators) are equivalent . The theory is developped for Fourier-Legendre expansions.
openaire   +2 more sources

Approximation theorems for Kantorovich type Lupaș-Stancu operators based on \(q\)-integers

Journal of Numerical Analysis and Approximation Theory, 2017
In this paper, we introduce a Kantorovich generalization of q-Stancu-Lupa¸s operators and investigate their approximation properties. The rate of convergence of these operators are obtained by means of modulus of continuity, functions of Lipschitz class
Sevilay Kirci Serenbay, Özge Dalmanoğlu   +1 more
doaj   +2 more sources

Bézier Form of Quantum λ‐Bernstein–Schurer Operators With Associated Approximation Properties

Journal of Mathematics, Volume 2026, Issue 1, 2026.
We introduce a Bézier form of Schurer‐type modification of the quantum λ‐Bernstein operators, extending the classical Schurer operators through the Bézier basis with shape parameter −1 ≤ λ ≤ 1. By applying Korovkin’s theorem, we obtain both global and local approximation results.
Jabr Aljedani, Md. Nasiruzzaman, S. A. Mohiuddine, Ding-Xuan Zhou   +3 more
wiley   +1 more source

Old and new on the Peetre K-functional and its relations to real interpolation theory, quasi-monotone functions and wavelets

Analysis and Mathematical Physics
Abstract The Peetre K-functional is a key object in the development of the real method of interpolation. In this paper we point out a less known relation to wavelet theory and its applications to approximation theory and engineering applications.
Rune Dalmo, Lars-Erik Persson, Natasha Samko   +2 more
openaire   +4 more sources

Metaplectic operators with quasi‐diagonal kernels

Mathematische Nachrichten, Volume 298, Issue 12, Page 3618-3638, December 2025.
Abstract Metaplectic operators form a relevant class of operators appearing in different applications, in this work we study their Schwartz kernels. Namely, diagonality of a kernel is defined by imposing rapid off‐diagonal decay conditions, and quasi‐diagonality by imposing the same conditions on the smoothing of the kernel through convolution with the
Gianluca Giacchi, Luigi Rodino
wiley   +1 more source

Approximation properties by shifted knots type of α-Bernstein–Kantorovich–Stancu operators

Journal of Inequalities and Applications
Through the real polynomials of the shifted knots, the α-Bernstein–Kantorovich operators are studied in their Stancu form, and the approximation properties are obtained.
Md. Nasiruzzaman, Mohammad Dilshad, Bader Mufadhi Eid Albalawi, Mohammad Rehan Ajmal   +3 more
doaj   +1 more source

ψ‐Bernstein–Kantorovich operators

Mathematical Methods in the Applied Sciences, Volume 48, Issue 1, Page 1124-1141, 15 January 2025.
In this article, we introduce a modified class of Bernstein–Kantorovich operators depending on an integrable function ψα$$ {\psi}_{\alpha } $$ and investigate their approximation properties. By choosing an appropriate function ψα$$ {\psi}_{\alpha } $$, the order of approximation of our operators to a function f$$ f $$ is at least as good as the ...
Hüseyin Aktuğlu, Mustafa Kara, Erdem Baytunç   +2 more
wiley   +1 more source

Approximation Properties of a New Class of Beta‐Type Szász–Mirakjan Operators

Journal of Mathematics, Volume 2025, Issue 1, 2025.
We use the new variant of Szász–Mirakjan operators to construct a generalized version of Szász‐beta type operators and obtain auxiliary lemmas. We present the weighted approximation theorems and, by using Peetre’s K‐function, the local approximation results of these operators are studied.
Md. Nasiruzzaman, Rubayyi T. Alqahtani, S. A. Mohiuddine, Ding-Xuan Zhou   +3 more
wiley   +1 more source

Approximation by Stancu-type α-Bernstein-Schurer-Kantorovich operators

Journal of Inequalities and Applications
In the present article, we study the approximation properties of constructed operators based on the shape parameter α. We construct the Stancu-type operators of α-Bernstein–Schurer–Kantorovich operators. Here the shape parameter α ∈ [ 0 , 1 ] $\alpha \in
Md. Nasiruzzaman
doaj   +1 more source

New estimates of Rychkov's universal extension operator for Lipschitz domains and some applications

Mathematische Nachrichten, Volume 297, Issue 4, Page 1407-1443, April 2024.
Abstract Given a bounded Lipschitz domain Ω⊂Rn$\Omega \subset \mathbb {R}^n$, Rychkov showed that there is a linear extension operator E$\mathcal {E}$ for Ω$\Omega$, which is bounded in Besov and Triebel‐Lizorkin spaces. In this paper, we introduce some new estimates for the extension operator E$\mathcal {E}$ and give some applications.
Ziming Shi, Liding Yao
wiley   +1 more source