Vector abstract fractional korovkin approximation

In this chapter we study quantitatively with rates the convergence of sequences of general Bochner type integral operators, applied on Banach space valued functions, to function values. The results are mainly pointwise, but in the application to vector Bernstein polynomials we end up to obtain a uniform estimate. To prove our main results we have to build a rich background containing many interesting vector fractional results. Our inequalities are fractional involving the right and left vector Caputo type fractional derivatives, built in vector moduli of continuity. We treat very general classes of Banach space valued functions. It follows [7]