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Remarks on uniformly bounded composition operator acting between Banach spaces of functions of two variables of bounded schramm Φ-variation

Ereú T., Merentes N., Wróbel M.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

2013

Vol. 18

19--27

In this paper we prove that if the composition operator H of generator h : Ib a × C → Y (X is a real normed space, Y is a real Banach space, C is a convex cone in X and Ib a ⸦ R2) maps Φ1 BV (Ib a, C) into Φ2 BV (Ib a, Y) and is uniformly bounded, then the left-left regularization h* of h is an affine function in the third variable.

Uniformly bounded set-valued composition operators in the spaces of functions of bounded variation in the sense of Schramm

Ereú T., Merentes N., Sanchez J. L., Wróbel M.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

2012

Vol. 17

37-47

We prove that, under some general assumptions, the one-sided regularizations of the generator of any uniformly bounded set-valued composition operator, acting in the spaces of functions of bounded variation in the sense of Schramm with nonempty bounded closed and convex values is an aﬃne function. As a special case, we obtain an earlier result ([15]).

Uniformly continuous set-valued composition operators in the spaces of functions of bounded variation in the sense of Schramm

Ereú T., Sánchez J. L., Merentes N., Wróbel M.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

2011

Vol. 16

23--32

We show that the one-sided regularizations of the generator of any uniformly continuous set-valued Nemytskij operator, acting between the spaces of functions of bounded variation in the sense of Schramm, is an affine function. Results along these lines extend the study [1].

Efficient Algorithm of Affine form Searching for Weakly Specified Boolean Function

Porwik P.

Fundamenta Informaticae

2007

Vol. 77, nr 3

277-291

This paper presents the spectral method of recognition of an incompletely defined Boolean function. The main goal of analysis is fast estimation whether a given single output function can be extended to affine form. Furthermore, a simple extension algorithm is proposed for functions, for which the affine form is reachable. The algorithm is compared with other methods. Theoretical and experimental results demonstrate the efficiency of the presented approach.