TL;DR
This paper investigates composite bivariate Bernstein operators and their associated cubature formulas, providing bounds on approximation errors and analyzing the non-multiplicativity of the integration functional.
Contribution
It introduces bounds for the remainder term of the cubature formula and examines the non-multiplicative nature of the integration functional in this context.
Findings
Upper bounds for the remainder term are established.
Results show the non-multiplicativity of the integration functional.
Analysis based on moduli of continuity of order two.
Abstract
We consider a sequence of composite bivariate Bernstein operators and the cubature formula associated with them. The upper bounds for the remainder term of the cubature formula are described in terms of moduli of continuity of order two. Also we include some results showing how non-multiplicative the integration functional is.
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