Version 1
: Received: 12 October 2024 / Approved: 12 October 2024 / Online: 15 October 2024 (03:40:12 CEST)
How to cite:
Karabıyık, Ü.; Karaisa, A.; Ayık, A. Some Approximation Properties of Two Dimensional Chlodovsky-Bernstein Operators Based on (P, Q) Integer. Preprints2024, 2024100977. https://doi.org/10.20944/preprints202410.0977.v1
Karabıyık, Ü.; Karaisa, A.; Ayık, A. Some Approximation Properties of Two Dimensional Chlodovsky-Bernstein Operators Based on (P, Q) Integer. Preprints 2024, 2024100977. https://doi.org/10.20944/preprints202410.0977.v1
Karabıyık, Ü.; Karaisa, A.; Ayık, A. Some Approximation Properties of Two Dimensional Chlodovsky-Bernstein Operators Based on (P, Q) Integer. Preprints2024, 2024100977. https://doi.org/10.20944/preprints202410.0977.v1
APA Style
Karabıyık, Ü., Karaisa, A., & Ayık, A. (2024). Some Approximation Properties of Two Dimensional Chlodovsky-Bernstein Operators Based on (P, Q) Integer. Preprints. https://doi.org/10.20944/preprints202410.0977.v1
Chicago/Turabian Style
Karabıyık, Ü., Ali Karaisa and Adem Ayık. 2024 "Some Approximation Properties of Two Dimensional Chlodovsky-Bernstein Operators Based on (P, Q) Integer" Preprints. https://doi.org/10.20944/preprints202410.0977.v1
Abstract
In the present study, we introduce the two dimensional Chlodovsky type Bernstein operators based on (p,q)−integer. We examine approximation properties of our new operator by the help of Korovkin-type theorem. Further, we present the local approximation properties and establish the rates of convergence by means of the modulus of continuity and the Lipschitz type maximal function. Also, we give a Voronovskaja type theorem for this operators. And, we investigate weighted approximation properties of these operators and estimate rate of convergence in the same space. Finally, with the help of Maple, illustrative graphics show the rate of convergence of these operators to certain functions . The optimization of approximation speeds by operators during system control provides significant improvements in stability and performance. As a result, the control and modeling of dynamic systems become more efficient and effective through innovative methods. These advancements in the fields of modeling fractional differential equations and control theory offer substantial benefits to both modeling and optimization processes, expanding the range of applications in these areas.
Keywords
Two dimensional (p,q)- Chlodovsky type Bernstein operators; Voronovskaja type theorem; (p,q)-integer; Control theory
Subject
Computer Science and Mathematics, Analysis
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
