Abstract and Applied Analysis

Abstract and Applied Analysis / 2003 / Article

Open Access

Volume 2003 |Article ID 417412 | https://doi.org/10.1155/S1085337503206011

Tzanko Donchev, Pando Georgiev, "Relaxed submonotone mappings", Abstract and Applied Analysis, vol. 2003, Article ID 417412, 13 pages, 2003. https://doi.org/10.1155/S1085337503206011

Relaxed submonotone mappings

Received30 Nov 2001

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.

Copyright © 2003 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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