TY - JOUR
T1 - Approximation by the modified λ-Bernstein-polynomial in terms of basis function
AU - Ayman-Mursaleen, Mohammad
AU - Nasiruzzaman, Md
AU - Rao, Nadeem
AU - Dilshad, Mohammad
AU - Nisar, Kottakkaran Sooppy
N1 - Publisher Copyright:
© 2024 the Author(s), licensee AIMS Press.
PY - 2024
Y1 - 2024
N2 - In this article by means of shifted knots properties, we introduce a new type of coupled Bernstein operators for Bézier basis functions. First, we construct the operators based on shifted knots properties of Bézier basis functions then investigate the Korovkin’s theorem, establish a local approximation theorem, and provide a convergence theorem for Lipschitz continuous functions and Peetre’s K-functional. In addition, we also obtain an asymptotic formula of the type Voronovskaja.
AB - In this article by means of shifted knots properties, we introduce a new type of coupled Bernstein operators for Bézier basis functions. First, we construct the operators based on shifted knots properties of Bézier basis functions then investigate the Korovkin’s theorem, establish a local approximation theorem, and provide a convergence theorem for Lipschitz continuous functions and Peetre’s K-functional. In addition, we also obtain an asymptotic formula of the type Voronovskaja.
KW - Bernstein-polynomial
KW - Bézier basis function
KW - Lipschitz maximal functions
KW - modulus of continuity
KW - Peetre’s K-functional
KW - shifted knots
KW - λ-Bernstein-polynomial
UR - https://www.scopus.com/pages/publications/85182641046
U2 - 10.3934/math.2024217
DO - 10.3934/math.2024217
M3 - Article
AN - SCOPUS:85182641046
SN - 2473-6988
VL - 9
SP - 4409
EP - 4426
JO - AIMS Mathematics
JF - AIMS Mathematics
IS - 2
ER -