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On Functions with the Cauchy Difference Bounded by a Functional

100%

Fechner W.

Bulletin of the Polish Academy of Sciences. Mathematics

2004

tom 52

nr 3

265-271

K. Baron and Z. Kominek [2] have studied the functional inequality f(x+y) - f(x) - f(y) ≥ ϕ (x,y), x, y ∈ X, under the assumptions that X is a real linear space, ϕ is homogeneous with respect to the second variable and f satisfies certain regularity conditions. In particular, they have shown that ϕ is bilinear and symmetric and f has a representation of the form f(x) = ½ ϕ(x,x) + L(x) for x ∈ X, where L is a linear function. The purpose of the present paper is to consider this functional inequality under different assumptions upon X, f and ϕ. In particular we will give conditions which force biadditivity and symmetry of ϕ and the representation f(x) = ½ ϕ(x,x) - A(x) for x ∈ X, where A is a subadditive function.

On the Stability of Orthogonal Additivity

63%

Fechner W., Sikorska J.

Bulletin of the Polish Academy of Sciences. Mathematics

2010

tom 58

nr 1

23-30

We deal with the stability of the orthogonal additivity equation, presenting a new approach to the proof of a 1995 result of R, Ger and the second author. We sharpen the estimate obtained there. Moreover, we work in more general settings, providing an axiomatic framework which covers much more cases than considered before by other authors.

Ograniczanie wyników

2 Bulletin of the Polish Academy of Sciences. Mathematics

2 Fechner W.

1 Sikorska J.

1 2010

1 2004

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On Functions with the Cauchy Difference Bounded by a Functional

On the Stability of Orthogonal Additivity