TY  - JOUR
ID  - Matkowski2011
LB  - Matkowski2011
AU  - Matkowski, Janusz
TI  - Subadditive periodic functions
ST  - Subadditive periodic functions
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2011
VL  - 31
IS  - 1
SP  - 75
EP  - 96
DO  - http://dx.doi.org/10.7494/OpMath.2011.31.1.75
UR  - http://dx.doi.org/10.7494/OpMath.2011.31.1.75
AB  - Some conditions under which any subadditive function is periodic are presented. It is shown that the boundedness from below in a neighborhood of a point of a subadditive periodic (s.p.) function implies its nonnegativity, and the boundedness from above in a neighborhood of a point implies it nonnegativity and global boundedness from above. A necessary and sufficient condition for existence of a subadditive periodic extension of a function \(f_{0}:[0,1)\rightarrow \mathbb{R}\) is given. The continuity, differentiability of a s.p. function is discussed, and an example of a continuous nowhere differentiable s.p. function is presented. The functions which are the sums of linear functions and s.p. functions are characterized. The refinements of some known results on the continuity of subadditive functions are presented.
KW  - subadditive function
KW  - periodic function
KW  - periodic extension
KW  - concave function
KW  - continuity
KW  - continuous nowhere differentiable function
SN  - 1232-9274
ER  -