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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
PubMed
Summary
This summary is machine-generated.

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.

Keywords:
Bézier basis functionsLipschitz continuous functionsModulus of continuityVoronovskaja asymptotic formulaλ-Bernstein operators

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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.