On the continuity ofQ-convex functions and additive functions
β Scribed by Zygfryd Kominek
- Publisher
- Springer
- Year
- 1981
- Tongue
- English
- Weight
- 210 KB
- Volume
- 23
- Category
- Article
- ISSN
- 0001-9054
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π SIMILAR VOLUMES
Let S q (n) denote the sum of digits of n in base q. For given pairwise coprime bases q 1 , ..., q l and arbitrary residue classes a i mod m i (i=1, ..., l), we obtain an estimate with error term O(N 1&$ ) for the quantity which extends results of J. Be sineau and establishes a conjecture of A. O.
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 β X (where X is a vector space) is said to be a convex cone if and only if C + C β C and t C β C for all t β (0, β). Definition 2.2.