Advertisement
Published in:
2011 | OriginalPaper | Chapter
Fractional Trigonometric Convergence Theory of Positive Linear Operators
Author : George A. Anastassiou
Published in: Intelligent Mathematics: Computational Analysis
Publisher: Springer Berlin Heidelberg
Activate our intelligent search to find suitable subject content or patents.
Select sections of text to find matching patents with Artificial Intelligence. powered by
Select sections of text to find additional relevant content using AI-assisted search. powered by
In this chapter we study quantitatively with rates the trigonometric weak convergence of a sequence of finite positive measures to the unit measure. Equivalently we study quantitatively the trigonometric pointwise convergence of sequence of positive linear operators to the unit operator, all acting on continuous functions on [ −
π
,
π
]. From there we obtain with rates the corresponding trigonometric uniform convergence of the latter. The 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 these uniform trigonometric Shisha-Mond type inequality we derive the trigonometric fractional Korovkin type theorem regarding the trigonometric uniform convergence of positive linear operators to the unit. We give applications, especially to Bernstein polynomials over [ −
π
,
π
] for which we establish fractional trigonometric quantitative results. This chapter relies on [46].