Opuscula Mathematica
Opuscula Math. 30, no. 3 (), 241-248
http://dx.doi.org/10.7494/OpMath.2010.30.3.241
Opuscula Mathematica

Uniformly continuous set-valued composition operators in the space of total φ-bidimensional variation in the sense of Riesz





Abstract. In this paper we prove that if a Nemytskij composition operator, generated by a function of three variables in which the third variable is a function one, maps a suitable large subset of the space of functions of bounded total \(\varphi\)-bidimensional variation in the sense of Riesz, into another such space, and is uniformly continuous, then its generator is an affine function in the function variable. This extends some previous results in the one-dimensional setting.
Keywords: \(\varphi\)-bidimensional variation, uniformly continuous, Nemytskij operator.
Mathematics Subject Classification: 47H30, 39B52.
Cite this article as:
Wadie Aziz, José Giménez, Nelson Merentes, José Luis Sánchez, Uniformly continuous set-valued composition operators in the space of total φ-bidimensional variation in the sense of Riesz, Opuscula Math. 30, no. 3 (2010), 241-248, http://dx.doi.org/10.7494/OpMath.2010.30.3.241
 
Download this article's citation as:
a .bib file (BibTeX), a .ris file (RefMan), a .enw file (EndNote)
or export to RefWorks.

RSS Feed

horizontal rule

ISSN 1232−9274, e-ISSN 2300−6919, DOI https://doi.org/10.7494/OpMath
Copyright © 2003−2017 OPUSCULA MATHEMATICA
Contact: opuscula@agh.edu.pl
Made by Tomasz Zabawa

horizontal rule

In accordance with EU legislation we advise you this website uses cookies to allow us to see how the site is used. All data is anonymized.
All recent versions of popular browsers give users a level of control over cookies. Users can set their browsers to accept or reject all, or certain, cookies.