Relaxed submonotone mappings

[摘要] The notions ofrelaxed submonotoneandrelaxedmonotonemappings 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. Forexample, 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.

[学科分类] 数学（综合）