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.
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页码：649 / 659
页数：11
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