SUBSTITUTION OPERATORS IN THE SPACES OF FUNCTIONS OF BOUNDED VARIATION BV2α(I)

Title & Authors
SUBSTITUTION OPERATORS IN THE SPACES OF FUNCTIONS OF BOUNDED VARIATION BV2α(I)
Aziz, Wadie; Guerrero, Jose Atilio; Merentes, Nelson;

Abstract
The space $\small{BV^2_{\alpha}(I)}$ of all the real functions defined on interval $\small{I=[a,b]{\subset}\mathbb{R}}$, which are of bounded second $\small{{\alpha}}$-variation (in the sense De la Vall$\small{\acute{e}}$ Poussin) on I forms a Banach space. In this space we define an operator of substitution H generated by a function $\small{h:I{\times}\mathbb{R}{\rightarrow}\mathbb{R}}$, and prove, in particular, that if H maps $\small{BV^2_{\alpha}(I)}$ into itself and is globally Lipschitz or uniformly continuous, then h is an affine function with respect to the second variable.
Keywords
variation in the sense of De la Vall$\small{\acute{e}}$e Poussin;uniformly continuous operator;Nemytskii (substitution) operator;Jensen equation;
Language
English
Cited by
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