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On some nonlinear operators in $${\varvec{\Lambda }} {\varvec{BV}}$$ΛBV-spaces

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In this paper we investigate autonomous as well as nonautonomous superposition operators acting between spaces of functions of bounded $$\Lambda $$Λ-variation. A particular emphasis is put on acting conditions as… Click to show full abstract

In this paper we investigate autonomous as well as nonautonomous superposition operators acting between spaces of functions of bounded $$\Lambda $$Λ-variation. A particular emphasis is put on acting conditions as well as on continuity problems for such operators. In particular, we give necessary and sufficient conditions for nonautonomous superposition operators to map a space of functions of bounded $$\Lambda $$Λ-variation into itself. Moreover, we prove the continuity of certain autonomous superposition operators acting between various spaces of functions of bounded $$\Lambda $$Λ-variation. We also examine the existence of $$\Lambda BV$$ΛBV-solutions as well as the topological structure of such solution sets to classical nonlinear integral equations.

Keywords: nonlinear operators; lambda variation; functions bounded; operators varvec; bounded lambda; superposition operators

Journal Title: Journal of Fixed Point Theory and Applications
Year Published: 2017

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