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Paper Information

Journal:   BANACH JOURNAL OF MATHEMATICAL ANALYSIS   2017 , Volume 11 , Number 1; Page(s) 130 To 142.
 
Paper: 

HLAWKA’S FUNCTIONAL INEQUALITY ON TOPOLOGICAL GROUPS

 
 
Author(s):  FECHNER WLODZIMIERZ*
 
* 
 
Abstract: 

Let (X,+)(X,+) be a topological abelian group. We discuss regularity of solutions f:X®Rf:X®R of Hlawka’s functional inequality f(x+y)+f(y+z)+f(x+z)£f(x+y+z)+f(x)+f(y)+f(z),f(x+y)+f(y+z)+f(x+z)?f(x+y+z)+f(x)+f(y)+f(z), postulated for all x,y,z?Xx,y,z?X. We study the lower and upper hull of ff. Moreover, we provide conditions which imply continuity of ff. We prove, in particular, that if XX is generated by any neighborhood of zero, f is continuous at zero, and f(0)=0f(0)=0, then f is continuous on X.

 
Keyword(s): FUNCTIONAL INEQUALITY, HLAWKA’S INEQUALITY, DRYGAS INEQUALITY, SUBQUADRATIC MAPPING
 
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