Fractional Korovkin theory

George A. Anastassiou

Chaos, Solitons & Fractals, 2009, vol. 42, issue 4, 2080-2094

Abstract: In this article we study quantitatively with rates the weak convergence of a sequence of finite positive measures to the unit measure. Equivalently we study quantitatively the pointwise convergence of sequence of positive linear operators to the unit operator, all acting on continuous functions. From there we derive with rates the corresponding uniform convergence of the last. Our inequalities for all of the above in their right hand sides contain the moduli of continuity of the right and left Caputo fractional derivatives of the involved function. From our uniform Shisha–Mond type inequality we derive the first fractional Korovkin type theorem regarding the uniform convergence of positive linear operators to the unit. We give applications, especially to Bernstein polynomials for which we establish fractional quantitative results.

Date: 2009
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0960077909003105
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:42:y:2009:i:4:p:2080-2094

DOI: 10.1016/j.chaos.2009.03.183

Access Statistics for this article

Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros

More articles in Chaos, Solitons & Fractals from Elsevier
Bibliographic data for series maintained by Thayer, Thomas R. ().