On a generalization of Bernstein-Chlodovsky operators for convex cones
Abstract
A sequence of positive linear operators acting on suitable function spaces on convex Borel cones is introduced and studied. Such operators generalize the well-known Bernstein-Chlodovsky operators on $[0,+\infty[$ and, in addition, they unify many of their more recent extensions to other settings. The study is mainly addressed to highlight their pointwise convergence as well as their uniform convergence on compact subsets for particular classes of bounded Borel measurable functions. In some particular cases, by means of such operators, a Weierstrass-type density result is obtained which concerns the approximation of such class of functions in terms of polynomials or, more generally, of elements of some function algebras. In order to achieve the main results some new Korovkin-type theorems are also discussed in the framework of completely regular spaces. In a final section, some examples and applications are discussed as well.
Keywords
References
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Details
Primary Language
English
Subjects
Approximation Theory and Asymptotic Methods
Journal Section
Research Article
Authors
Early Pub Date
December 16, 2025
Publication Date
December 16, 2025
Submission Date
July 16, 2025
Acceptance Date
October 27, 2025
Published in Issue
Year 2025 Volume: 8 Number: Special Issue: ICCMA
APA
Altomare, F. (2025). On a generalization of Bernstein-Chlodovsky operators for convex cones. Constructive Mathematical Analysis, 8(Special Issue: ICCMA), 1-17. https://doi.org/10.33205/cma.1744040
AMA
1.Altomare F. On a generalization of Bernstein-Chlodovsky operators for convex cones. CMA. 2025;8(Special Issue: ICCMA):1-17. doi:10.33205/cma.1744040
Chicago
Altomare, Francesco. 2025. “On a Generalization of Bernstein-Chlodovsky Operators for Convex Cones”. Constructive Mathematical Analysis 8 (Special Issue: ICCMA): 1-17. https://doi.org/10.33205/cma.1744040.
EndNote
Altomare F (December 1, 2025) On a generalization of Bernstein-Chlodovsky operators for convex cones. Constructive Mathematical Analysis 8 Special Issue: ICCMA 1–17.
IEEE
[1]F. Altomare, “On a generalization of Bernstein-Chlodovsky operators for convex cones”, CMA, vol. 8, no. Special Issue: ICCMA, pp. 1–17, Dec. 2025, doi: 10.33205/cma.1744040.
ISNAD
Altomare, Francesco. “On a Generalization of Bernstein-Chlodovsky Operators for Convex Cones”. Constructive Mathematical Analysis 8/Special Issue: ICCMA (December 1, 2025): 1-17. https://doi.org/10.33205/cma.1744040.
JAMA
1.Altomare F. On a generalization of Bernstein-Chlodovsky operators for convex cones. CMA. 2025;8:1–17.
MLA
Altomare, Francesco. “On a Generalization of Bernstein-Chlodovsky Operators for Convex Cones”. Constructive Mathematical Analysis, vol. 8, no. Special Issue: ICCMA, Dec. 2025, pp. 1-17, doi:10.33205/cma.1744040.
Vancouver
1.Francesco Altomare. On a generalization of Bernstein-Chlodovsky operators for convex cones. CMA. 2025 Dec. 1;8(Special Issue: ICCMA):1-17. doi:10.33205/cma.1744040
