Cone monotone mappings: continuity and differentiability

Details Cone monotone mappings: continuity and differentiability Cone monotone mappings: continuity and differentiability

2005-10-31

arxiv.org/abs/math/0510678v2

Mathematics

Functional Analysis

13 pages; updated version

Scientific paper

We generalize some results of Borwein, Burke, Lewis, and Wang to mappings with values in metric (resp. ordered normed linear) spaces. We define two classes of monotone mappings between an ordered linear space and a metric space (resp. ordered linear space): $K$-monotone dominated and cone-to-cone monotone mappings. First we show some relationships between these classes. Then, we study continuity and differentiability (also in the metric and $w^*$ senses) of mappings in these classes.

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