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ON APPROXIMATELY SUBADDITIVE FUNCTIONS

1990
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Demonstratio Mathematica
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Let (X,+) be a commutative, 2-divisible group. Than every approximately subadditive functional (i.e. f» X -*• 1R, R denotes the real line, such that f(x+y)< f(x)+f(y)+ £ for some £>0 and all i,;el), is minorized by a Jensen functional. Moreover, if fs X-"-Ris approximately convex (in the sense of Jensen) function, then there exists convex (in the sense of Jensen) function hi X -»R and a constant K suoh that |f-h|-$K. In 1952 D.H. Hyers and S.M. Ulam ([2]) proved the stability of the inequality

doi:10.1515/dema-1990-0116
fatcat:v3e4yvgdzjad5jufwzwnmvsmk4