Year: 2022
Type: preprint
Abstract: We construct and study sequences of linear operators of Bernstein-type acting on bivariate functions defined on the unit disk. To this end, we study Bernstein-type operators under a domain transformation, we analyse the bivariate Bernstein-Stancu operators, and we introduce Bernstein-type operators on disk quadrants by means of continuously differentiable transformations of the function. We state convergence results for continuous functions and we estimate the rate of convergence. Finally some interesting numerical examples are given, comparing approximations using the shifted Bernstein-Stancu and the Bernstein-type operator on disk quadrants.
Source: arXiv (Cornell University)
Institution: Universidad de Granada
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G1024557734, G1228787638, G1650125035, G1855990336, G1953074864, G21826877, G2193086574, G2262748287, G2756482649, G3480869486, G3518538256, G425668148, G4606149875, G4668258890, G4835773514, G4893791014, G490073602, G5421974903, G5635532810, G567365627, G597010865, G6728930308, G6958561662, G7863371703, G8178315791, G8497050386
OpenAlex ID: W4221138580