Approximation of functions by Stancu variant of Bernstein–Kantorovich operators based on shape parameter α

We construct the Stancu variant of Bernstein–Kantorovich operators based on shape parameter α . We investigate the rate of convergence of these operators by means of suitable modulus of continuity to any continuous functions f ( x ) on x ∈ [ 0 , 1 ] and Voronovskaja-type approximation theorem. Moreo...

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Bibliographic Details
Published inRevista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas Vol. 114; no. 2
Main Authors Mohiuddine, S. A., Özger, Faruk
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 2020
Springer Nature B.V
Subjects
Applications of Mathematics
Approximation
Continuity (mathematics)
Convergence
Mathematical analysis
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Operators (mathematics)
Original Paper
Parameters
Theoretical
Bernstein–Kantorovich operators
41A36
Weighted approximation
Secondary 41A35
Rate of convergence
Primary 41A25
Pointwise convergence
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Summary:We construct the Stancu variant of Bernstein–Kantorovich operators based on shape parameter α . We investigate the rate of convergence of these operators by means of suitable modulus of continuity to any continuous functions f ( x ) on x ∈ [ 0 , 1 ] and Voronovskaja-type approximation theorem. Moreover, we study other approximation properties of our new operators such as weighted approximation as well as pointwise convergence. Finally, some illustrative graphics are provided here by our new Stancu-type Bernstein–Kantorovich operators in order to demonstrate the significance of our operators.
ISSN:1578-7303
1579-1505
DOI:10.1007/s13398-020-00802-w