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Pointwise approximation by a Durrmeyer variant of Bernstein-Stancu operators
1Department of Mathematics, Hangzhou Normal University, Hangzhou, Zhejiang 310036 China.
Journal of Inequalities and Applications
|February 14, 2017
Summary
This study introduces a new type of Durrmeyer variant of Bernstein-Stancu operators. Researchers established direct and converse approximation theorems for these novel operators.
Area of Science:
- Mathematical analysis
- Approximation theory
Background:
- Bernstein-Stancu operators are fundamental in approximation theory.
- Durrmeyer variants offer enhanced approximation properties.
Purpose of the Study:
- To introduce a novel Durrmeyer variant of Bernstein-Stancu operators.
- To investigate the approximation properties of these new operators.
Main Methods:
- Construction of Durrmeyer variant Bernstein-Stancu operators.
- Application of approximation theory techniques to derive direct and converse theorems.
Main Results:
- The paper presents the definition of the new operators.
- Direct approximation theorems are established for these operators.
- Converse approximation theorems are also obtained, detailing the sharpness of the approximation.
Conclusions:
- The introduced operators provide a new tool for approximation.
- The direct and converse theorems offer a comprehensive understanding of their approximation capabilities.
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