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SUBSTITUTION OPERATORS IN THE SPACES OF FUNCTIONS OF BOUNDED VARIATION BVα2 (I)

Wadie Aziz|Jos´e Atilio Guerrero|Nelson Merentes
대한수학회 (The Korean Mathematical Society)|2015.03|대한수학회보 (Bulletin of the KMS)|제52권 제2호|pp. 649-659

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참고문헌

키워드

Jensen equationvariation in the sense of De la Vall´ee Poussinuniformly continuous operatorNemytskii (substitution) operator
주제분류수학

초록

The space BVα2 (I) of all the real functions defined on interval I = [a, b] ⊂ R, which are of bounded second α-variation (in the sense De la Vall´e Poussin) on I forms a Banach space. In this space we define an operator of substitution H generated by a function h : I × R → R, and prove, in particular, that if H maps BVα2 (I) into itself and is globally Lipschitz or uniformly continuous, then h is an affine function with respect to the second variable.

Abstract

The space BVα2 (I) of all the real functions defined on interval I = [a, b] ⊂ R, which are of bounded second α-variation (in the sense De la Vall´e Poussin) on I forms a Banach space. In this space we define an operator of substitution H generated by a function h : I × R → R, and prove, in particular, that if H maps BVα2 (I) into itself and is globally Lipschitz or uniformly continuous, then h is an affine function with respect to the second variable.

참고문헌 (20)

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