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

被引：1

作者：

Aziz, Wadie ^{[1
]}

Guerrero, Jose Atilio ^{[2
]}

Merentes, Nelson ^{[3
]}

机构：

[1] Univ Los Andes, Dept Fis & Matemat, Trujillo, Venezuela

[2] Univ Nacl Expt Tachira, Dept Fis & Matemat, San Cristobal, Venezuela

[3] Cent Univ Venezuela, Escuela Matemat, Caracas, Venezuela

来源：

BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY | 2015年 / 52卷 / 02期

关键词：

variation in the sense of De la Vallee Poussin; uniformly continuous operator; Nemytskii (substitution) operator; Jensen equation; CONTINUOUS SUPERPOSITION OPERATORS;

D O I：

10.4134/BKMS.2015.52.2.649

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The space BV alpha 2 (I) of all the real functions defined on interval I = [a, b] subset of R, which are of bounded second a-variation (in the sense De la Valle Poussin) on I forms a Banach space. In this space we define an operator of substitution H generated by a function h : I x R --> R and prove, in particular, that if H maps BV alpha 2 (I) into itself and is globally Lipschitz or uniformly continuous, then h is an affine function with respect to the second variable.

引用

页码：649 / 659

页数：11

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