Topics in Contemporary Mathematical Analysis and Applications

3 Approximation by Kantorovich Variant of λ— Schurer Operators and Related Numerical Results

Faruk Özger

İzmir Katip Çelebi University

Kamil Demirci and Sevda Y⍳ld⍳z

Sinop University

CONTENTS

3.1     Introduction

3.2     Auxiliary Results

3.3     Approximation Behavior of λ-Schurer-Kantorovich Operators

3.4     Voronovskaja-type Approximation Theorems

3.5     Graphical and Numerical Results

3.6     Conclusion

References

3.1     Introduction

Functions have been widely approximated by positive linear operators over the past decades. Sergei Natanovich Bernstein first used the known polynomials in the approximation theory to prove Weierstrass’ well-known theorem [6]. Bernstein polynomials of order n are given by

$B_n(h;z)={\displaystyle \mathrm{\sum }_{i=0}^n\left(\begin{array}{c}n\\ i\end{array}\right)}{z}^i {(1-z)}^{n-i}h$