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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].

Functions of two variables with bounded φ-variation in the sense of Riesz

Aziz W., Leiva H., Merentes N., Sánchez J. L.

Journal of Mathematics and Applications

2010

Vol. 32

5-23

In this paper we introduce the concept of bounded φ- variation function, in the sense of Riesz, dened in a rectangle [wzór]. We prove that the linear space [wzór] generated by the class [wzór] of all φ-bounded variation functions is a Banach algebra. Moreover, we give necessary and sucient conditions for the Nemytskii operator acting in the space [wzór] to be globally Lipschitz.