Institute of Mathematics with Computer Center at the Bulgarian Academy of Sciences
Citation:
Preprint
Series/Report no.:
1993;11
Abstract:
The notions "submonotone" and "strictly submonotone" mapping, introduced by J. Spingarn in R^n, are extended by a natural way to arbitrary Banach spaces. Some results about monotone operators are proved for submonotone and strictly submonotone ones: Rockafellar’s result about locally boundedness of monotone operators; Kenderov’s result about single-valuedness and upper-semicontinuity almost everywhere of monotone operators in Asplund spaces and spaces with strictly convex duals. It is shown that subdifferentials of various closses non-convex functions possess submonotone properties. Results about generic differentiability of such functions are obtained (among them is a Zajisek’s and a new generalization of an Ekeland and Lebourg’s theorem)
