Geodesic
Better numerical approximation by λ-Durrmeyer-Bernstein type operators
Filomat, Tome 35 (2021) no. 4, p. 1405

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DOI

The main object of this paper is to construct a new Durrmeyer variant of the λ-Bernstein type operators which have better features than the classical one. Some results concerning the rate of convergence in terms of the first and second moduli of continuity and asymptotic formulas of these operators are given. Moreover, we define a bivariate case of these operators and investigate the approximation degree by means of the total and partial modulus of continuity and the Peetre's K-functional. A Voronovskaja type asymptotic and Grüss-Voronovskaja theorem for the bivariate operators is also proven. Further, we introduce the associated GBS (Generalized Boolean Sum) operators and determine the order of convergence with the aid of the mixed modulus of smoothness for the Bögel continuous and Bögel differentiable functions. Finally the theoretical results are analyzed by numerical examples
DOI : 10.2298/FIL2104405R
Classification : 41A25, 26A15
Keywords: λ-Bernstein operators, Durrmeyer operators, Generalized Boolean sum operators, rate of convergence, Voronovskaja type theorem, total modulus of continuity, partial modulus of continuity, mixed modulus of smoothness 
Voichiţa Adriana Radu; Purshottam Narain Agrawal; Jitendra Kumar Singh. Better numerical approximation by λ-Durrmeyer-Bernstein type operators. Filomat, Tome 35 (2021) no. 4, p. 1405 . doi: 10.2298/FIL2104405R
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     title = {Better numerical approximation by {\ensuremath{\lambda}-Durrmeyer-Bernstein} type operators},
     journal = {Filomat},
     pages = {1405 },
     year = {2021},
     volume = {35},
     number = {4},
     doi = {10.2298/FIL2104405R},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2104405R/}
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