Abstract and Applied Analysis
Volume 2003 (2003), Issue 1, Pages 19-31
doi:10.1155/S1085337503206011
Relaxed submonotone mappings
Tzanko Donchev1
and Pando Georgiev2
1Department of Mathematics, University of Architecture, Civil Engineering and Geodesy, 1 Christo Smirnenski blvd., Sofia 1046, Bulgaria
2Faculty of Mathematics and Informatics, Sofia University St. Kliment Ohridski, Department of Operational Research, Sofia 1126, Bulgaria
Abstract
The notions of relaxed submonotone and relaxed monotone mappings in Banach spaces are introduced and many of their properties are investigated. For example, the Clarke subdifferential of a locally Lipschitz function in a separable Banach space is relaxed submonotone on a residual subset. For example, it is shown that this property need not be valid on the whole space. We prove, under certain hypotheses, the surjectivity of the relaxed monotone mappings.