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Approximation properties of λ-Bernstein operators
Qing-Bo Cai1, Bo-Yong Lian2, Guorong Zhou3
11School of Mathematics and Computer Science, Quanzhou Normal University, Quanzhou, China.
Journal of Inequalities and Applications
|March 27, 2018
Summary
This study introduces new lambda-Bernstein operators, demonstrating their effectiveness in approximation theorems and convergence for functions. Numerical examples show improved approximation accuracy compared to existing methods.
Area of Science:
- Mathematical Analysis
- Approximation Theory
Background:
- Bernstein operators are fundamental in approximation theory.
- There is ongoing research to enhance the properties and convergence rates of these operators.
Purpose of the Study:
- Introduce a new family of lambda-Bernstein operators.
- Investigate the approximation properties of these novel operators.
Main Methods:
- Utilized Korovkin-type approximation theorems.
- Established local and Lipschitz continuity convergence theorems.
- Derived a Voronovskaja-type asymptotic formula.
Main Results:
- Demonstrated convergence of the new operators.
- Presented graphical and numerical evidence of approximation.
- Showcased potentially smaller approximation errors in specific cases.
Conclusions:
- The new lambda-Bernstein operators offer a valuable tool for approximation.
- The findings contribute to the advancement of approximation theory.
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