Regularity of weakly subquadratic functions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:382

Article

Gilanyi, Attila¹  Troczka-Pawelec, Katarzyna² 

[1] Univ Debrecen, Fac Informat, H-4010 Debrecen, Hungary

[2] Jan Dlugosz Univ Czestochowa, Inst Math & Comp Sci, PL-42200 Czestochowa, Poland

关键词: Subquadratic function;    Regularity theory;    Quadratic function;    Subadditive function;    Convex function;   

DOI  :  10.1016/j.jmaa.2011.04.073

来源: Elsevier

【 摘 要 】

Related to the theory of convex and subadditive functions, we investigate weakly subquadratic mappings, that is, solutions of the inequality f (x + y) f (x - y) <= (x) + 2f (y) (x, y is an element of G) for real-valued functions defined on a topological group G = (G, +). Especially, we study the lower and upper hulls of such functions and we prove Bernstein-Doetsch type theorems for them. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free