Approximation of Lebesgue integrable functions by Bernstein-Lototsky-Kantorovich operators

Khan, Asif; Iliyas, Mohammad; Mursaleen, M.

doi:10.1007/s12215-022-00747-6

Cited by 3 publications

(1 citation statement)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We note that additional classes of approximation algorithms should be also considered as practical tools for the approximation of nonlocal operators; see as examples [13] and techniques based on artificial neural networks [14,15].…”

Section: Introductionmentioning

confidence: 99%

On a Framework for the Stability and Convergence Analysis of Discrete Schemes for Nonstationary Nonlocal Problems of Parabolic Type

Čiegis

Dapšys

2022

Mathematics

View full text Add to dashboard Cite

The main aim of this article is to propose a general framework for the theoretical analysis of discrete schemes used to solve multi-dimensional parabolic problems with fractional power elliptic operators. This analysis is split into three parts. The first part is based on techniques well developed for the solution of nonlocal elliptic problems. The obtained discrete elliptic operators are used to formulate semi-discrete approximations. Next, the fully discrete schemes are constructed by applying the classical and robust approximations of time derivatives. The existing stability and convergence results are directly included in the new framework. In the third part, approximations of transfer operators are constructed by using uniform and the best uniform rational approximations. The stability and accuracy of the obtained local discrete schemes are investigated. The results of computational experiments are presented and analyzed. A three-dimensional test problem is solved. The rational approximations are constructed by using the BRASIL algorithm.

show abstract

Section: Introductionmentioning

confidence: 99%

On a Framework for the Stability and Convergence Analysis of Discrete Schemes for Nonstationary Nonlocal Problems of Parabolic Type

Čiegis

Dapšys

2022

Mathematics

View full text Add to dashboard Cite

show abstract

Approximation by a new kind of $$(\lambda ,\mu )$$-Bernstein–Kantorovich operators

Cai

2024

Comp. Appl. Math.

View full text Add to dashboard Cite

Approximation properties and q-statistical convergence of Kantorovich variant of Stancu type Lupaş operators

Malik,

Khan,

Mursaleen

2023

Filomat

View full text Add to dashboard Cite

We introduce Kantorovich variant of Stancu-Lupas? operators and study convergence and qstatistical convergence properties using Korovkin theorem. Rate of convergence is analyzed in terms of modulus of continuity, elements of Lipschitz class and Peetre?s K-functional. Direct theorems are proved and Voronovskaja type theorem is established. Graphical analysis of convergence and error estimations are presented with the help of MATLAB.

show abstract

Approximation of Lebesgue integrable functions by Bernstein-Lototsky-Kantorovich operators

Cited by 3 publications

References 6 publications

On a Framework for the Stability and Convergence Analysis of Discrete Schemes for Nonstationary Nonlocal Problems of Parabolic Type

On a Framework for the Stability and Convergence Analysis of Discrete Schemes for Nonstationary Nonlocal Problems of Parabolic Type

Approximation by a new kind of $$(\lambda ,\mu )$$-Bernstein–Kantorovich operators

Approximation properties and q-statistical convergence of Kantorovich variant of Stancu type Lupaş operators

Contact Info

Product

Resources

About