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Vectorial generalized g–fractional direct and iterated approximations by linear operators

Anastassiou George A.

Fasciculi Mathematici

2020

nr 64

17--42

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.

Integral of function with values in complete modular space

Liskowski M.

Demonstratio Mathematica

2002

Vol. 35, nr 2

347-356

The theorem on existence of an integral of a function with values in a modular space and some fundamental properties of this integral are given.

Remarks on set valued integrals of multifunctions with non empty bounded closed and convex values

Sambucini A.R.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

1999

[Z] 39

153-165

We study the comparison between the Aumann and the Bochner integrals for integrably non empty bounded closed convex valued multifunctions in a separable Banach space when it is not possible to apply embedding theoremes.