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On Extension and Continuity of p–Additive Functions

✍ Scribed by Joanna Szczawińska

Publisher
John Wiley and Sons
Year
2000
Tongue
English
Weight
168 KB
Volume
216
Category
Article
ISSN
0025-584X

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✦ Synopsis

In this paper we prove some properties of p -additive functions as well as p -additive set -valued functions.

We start with some definitions. Definition 2.1. A set C ⊆ X (where X is a vector space) is said to be a convex cone if and only if C + C ⊆ C and t C ⊆ C for all t ∈ (0, ∞). Definition 2.2. Let X 1 , . . . , X p , Z be real vector spaces and C 1 , . . . , C p be convex cones in X 1 , . . . , X p , respectively. We say that a function f :

and only if f is additive with respect to each variable.

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