Vector fractional trigonometric Korovkin approximation
In this manuscript we study quantitatively with rates the trigonometric fractional convergence of sequences of linear operators applied on Banach space valued functions. We derive pointwise and uniform estimates. To establish our main results we apply an elegant boundedness property of our linear operators by their companion positive linear operators. Our inequalities are trigonometric fractional involving the right and left vector Caputo type fractional derivatives, built in vector moduli of continuity. We consider very general classes of Banach space valued functions. Finally we present applications to vector Bernstein operators.
Progress in Fractional Differentiation and Applications
Anastassiou, G. (2017). Vector fractional trigonometric Korovkin approximation. Progress in Fractional Differentiation and Applications, 3 (4), 237-254. https://doi.org/10.18576/pfda/030401