On continuity and compactness of some nonlinear operators in the spaces of functions of bounded variation

被引：13

作者：

Bugajewski, Dariusz ^{[1
]}

Gulgowski, Jacek ^{[2
]}

Kasprzak, Piotr ^{[1
]}

机构：

[1] Adam Mickiewicz Univ, Fac Math & Comp Sci, Optimizat & Control Theory Dept, Ul Umultowska 87, PL-61614 Poznan, Poland

[2] Univ Gdansk, Inst Math, Ul Wita Stwosza 57, PL-80952 Gdansk, Poland

来源：

ANNALI DI MATEMATICA PURA ED APPLICATA | 2016年 / 195卷 / 05期

关键词：

Acting condition; Aronszajn-type theorem; Autonomous (nonautonomous); superposition operator; Bernstein polynomials; Compact operator; Hammerstein integral equation; Linear integral operator; Locally bounded mapping; Modulus of continuity; p-variation; Positive solution; R-delta-set; Variation in the sense of Jordan; Volterra-Hammerstein integral equation; phi-function; phi-variation; CONVERGENCE;

D O I：

10.1007/s10231-015-0526-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we deal with one of the basic problems of the theory of autonomous superposition operators acting in the spaces of functions of bounded variation, namely the problem concerning their continuity. We basically consider autonomous superposition operators generated by analytic functions or functions of C-1-class. We also investigate the problem of compactness of some classical linear and nonlinear operators acting in the space of functions of bounded variation in the sense of Jordan. We apply our results to the examination of the existence and the topological properties of solutions to nonlinear equations in those spaces.

引用

页码：1513 / 1530

页数：18

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