Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4615172 | Journal of Mathematical Analysis and Applications | 2015 | 6 Pages |
Abstract
We consider the multivariate Bernstein–Durrmeyer operator Mn,μMn,μ in terms of the Choquet integral with respect to a monotone and submodular set function μ on the standard d -dimensional simplex. This operator is nonlinear and generalizes the Bernstein–Durrmeyer linear operator with respect to a nonnegative, bounded Borel measure (including the Lebesgue measure). We prove uniform and pointwise convergence of Mn,μ(f)(x)Mn,μ(f)(x) to f(x)f(x) as n→∞n→∞, generalizing thus the results obtained in the recent papers [1] and [2].
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Sorin G. Gal, Bogdan D. Opris,