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Some approximation properties by a class of bivariate operators
Author(s) -
Acu Ana Maria,
Acar Tuncer,
Muraru CarmenVioleta,
Radu Voichiţa Adriana
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5515
Subject(s) - mathematics , bivariate analysis , generalization , operator (biology) , convergence (economics) , operator norm , class (philosophy) , type (biology) , operator theory , order (exchange) , space (punctuation) , pure mathematics , algebra over a field , discrete mathematics , mathematical analysis , statistics , artificial intelligence , computer science , philosophy , repressor , economic growth , ecology , linguistics , chemistry , biology , biochemistry , transcription factor , finance , economics , gene
Starting with the well‐ known Bernstein operators, in the present paper, we give a new generalization of the bivariate type. The approximation properties of this new class of bivariate operators are studied. Also, the extension of the proposed operators, namely, the generalized Boolean sum (GBS) in the Bögel space of continuous functions is given. In order to underline the fact that in this particular case, GBS operator has better order of convergence than the original ones, some numerical examples are provided with the aid of Maple soft. Also, the error of approximation for the modified Bernstein operators and its GBS‐type operator are compared.