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On functions with the cauchy difference bounded by a functional. III

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Abstract

We are going to discuss special cases of a conditional functional inequality

$$x \bot y \Rightarrow f(x + y) - f(x) - f(y) \geqslant 0, x, y \in X,$$

whereX is a real inner product space. In particular, we will give conditions which force the representationf(x)=c‖x‖2+a(x) for x ∈X, where c ∈ R anda:x→ℝ is an additive functional.

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Authors and Affiliations

  1. Institute of Mathematics, Silesian University, Bankowa 14, 40-007, Katowice, Poland

    W. Fechner

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  1. W. Fechner
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Correspondence to W. Fechner.

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Communicated by: A. Kreuzer

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Fechner, W. On functions with the cauchy difference bounded by a functional. III. Abh.Math.Semin.Univ.Hambg. 76, 57–62 (2006). https://doi.org/10.1007/BF02960854

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  • DOI: https://doi.org/10.1007/BF02960854

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