JournalszaaVol. 33, No. 1pp. 119–123

A Note on the Composition of Regular Functions

  • Wadie Aziz

    Universidad de los Andes, Trujillo, Venezuela
  • Nelson Merentes

    Central University of Venezuela, Caracas, Venezuela
  • José Luis Sánchez

    Central University of Venezuela, Caracas, Venezuela
A Note on the Composition of Regular Functions cover
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Abstract

In this note we give a condition on a function h:RRh:\mathbb{R}\rightarrow\mathbb{R}, both necessary and sufficient, under which the nonlinear composition operator Hf=hfHf = h \circ f maps the space of all regular functions f:[a,b]Rf : [a,b] \rightarrow \mathbb{R} into itself. Moreover, we show that in this case the operator HH is automatically bounded in the supremum norm.

Cite this article

Wadie Aziz, Nelson Merentes, José Luis Sánchez, A Note on the Composition of Regular Functions. Z. Anal. Anwend. 33 (2014), no. 1, pp. 119–123

DOI 10.4171/ZAA/1502