Approximation of functions by a class of Durrmeyer–Stancu type operators which includes Euler’s beta function

In this work, we construct the genuine Durrmeyer–Stancu type operators depending on parameter α in [ 0 , 1 ] as well as ρ > 0 and study some useful basic properties of the operators. We also obtain Grüss–Voronovskaja and quantitative Voronovskaja types approximation theorems for the aforesaid ope...

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Bibliographic Details
Published in:Advances in difference equations Vol. 2021; no. 1; pp. 1 - 14
Main Authors: Alotaibi, Abdullah, Özger, Faruk, Mohiuddine, S. A., Alghamdi, Mohammed A.
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 07.01.2021
Springer Nature B.V
SpringerOpen
Subjects:
Analysis
Applications
Approximation
Beta function
Difference and Functional Equations
Durrmeyer operators
Functional Analysis
Jacobi weights
Mathematics
Mathematics and Statistics
Methods
Modulus of continuity
Operators (mathematics)
Ordinary Differential Equations
Partial Differential Equations
Topics in Special Functions and q-Special Functions: Theory
Voronovskaja-type result
α-Bernstein operators
Bernstein operators
41A35
41A36
Durrmeyer operators
Voronovskaja-type result
41A10
Beta function
Jacobi weights
Modulus of continuity
ISSN:1687-1847, 1687-1839, 1687-1847
Online Access:Get full text
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Summary:In this work, we construct the genuine Durrmeyer–Stancu type operators depending on parameter α in [ 0 , 1 ] as well as ρ > 0 and study some useful basic properties of the operators. We also obtain Grüss–Voronovskaja and quantitative Voronovskaja types approximation theorems for the aforesaid operators. Further, we present numerical and geometrical approaches to illustrate the significance of our new operators.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1687-1847
1687-1839
1687-1847
DOI:10.1186/s13662-020-03164-0