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Univariate right fractional polynomial high order monotone approxi mation

Anastassiou G. A.

Demonstratio Mathematica

2016

Vol. 49, nr 1

1--10

Let (…) and let L* be a linear right fractional differential operator such that L*(f) ≥ 0 throughout [-1, 0]. We can find a sequence of polynomials Qn of degree ≤ n such that L*(Qn)≥ 0 over [-1, 0], furthermore f is approximated right fractionally and simultaneously by Qn on [-1, 1]. The degree of these restricted approximations is given via inequalities using a higher order modulus of smoothness for f(r).

Applications of the Rådström–Hörmander Embedding Theorem to Multifunctions

Kucia M.

Bulletin of the Polish Academy of Sciences. Mathematics

2005

Vol. 53, no 3

259-271

Using the Rådström–Hörmander theorem on embedding of the hyperspace of closed convex sets in a Banach space, we prove multivalued versions of some results known for real functions.

Some results on Carathéodory type multifunctions

Kucia A., Nowak A.

Bulletin of the Polish Academy of Sciences. Mathematics

2003

Vol. 51, no 3

283-290

We study the existence of multivalued Caratheodory type selections and the approximation of upper Caratheodory multifunctions. Our basie tool is the Marczewski function, i.e. the characteristic function of a sequence of sets.