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Approximation degree of Durrmeyer-Bézier type operators
Purshottam N Agrawal1, Serkan Araci2, Martin Bohner3
11Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, India.
Journal of Inequalities and Applications
|March 6, 2018
Summary
This study introduces Bézier variants of mixed hybrid operators, generalizing existing mathematical operators. The research investigates approximation properties and convergence rates for these new operators.
Area of Science:
- Approximation Theory
- Numerical Analysis
- Mathematical Operators
Background:
- Mixed hybrid operators generalize Phillips and Baskakov-Szász operators.
- Bézier variants offer new avenues for approximation analysis.
Purpose of the Study:
- To introduce and analyze Bézier variants of mixed hybrid operators.
- To investigate the approximation capabilities of these novel operators.
- To establish convergence rates and direct approximation theorems.
Main Methods:
- Utilizing Lipschitz class functions and modulus of continuity.
- Applying a weighted space approach.
- Employing the unified Ditzian-Totik modulus of smoothness.
- Analyzing functions with derivatives of bounded variation.
Main Results:
- Established degree of approximation for the new operators.
- Developed a direct approximation theorem.
- Determined the rate of convergence for specific function classes.
Conclusions:
- The Bézier variant of mixed hybrid operators exhibits significant approximation properties.
- The study provides a comprehensive analysis of convergence rates and approximation theorems.
- These findings contribute to the understanding of advanced mathematical operators in approximation theory.
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