Vectorial generalized g-fractional direct and iterated approximations by linear operators
2020
scientific article
english
- vector generalized g-direct and iterated fractional derivatives
- Bochner integral
- vector generalized g-direct and iterated fractional Taylor formulae
- vector modulus of continuity
- vector linear operators
- positive linear operators
- quantitative approximations
EN In this work we consider quantitatively with rates the convergence of sequences of linear operators applied on Banach space valued functions. The results are pointwise estimates with rates. To prove our main results we use an elegant and natural boundedness property of our linear operators by their companion positive linear operators. Our inequalities are generalized g-direct and iterated fractional involving the right and left vector Caputo type generalized g-direct and iterated fractional derivatives, built in vector moduli of continuity. We treat wide and general classes of Banach space valued functions. We give applications to vectorial Bernstein operators.
17 - 42
CC BY-NC-ND (attribution - noncommercial - no derivatives)
public
5
5