On continuity and compactness of some nonlinear operators in the spaces of functions of bounded variation
Dariusz Bugajewski , Jacek Gulgowski , Piotr Kasprzak
AbstractIn 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 C1-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.
|Journal series||Annali di Matematica Pura Ed Applicata, ISSN 0373-3114|
|Publication size in sheets||0.85|
|Keywords in English||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, Rδ-set, variation in the sense of Jordan, Volterra-Hammerstein integral equation, φ-function, φ-variation|
|License||Other; published final; ; with publication|
|Score|| = 30.0, 20-12-2017, ArticleFromJournal|
= 35.0, 20-12-2017, ArticleFromJournal
|Publication indicators||: 2016 = 0.864 (2) - 2016=0.968 (5)|
* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.