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Characterization of affine differences and related forms

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Abstract

In the present paper we consider the problem of characterization of maps which can be expressed as an affine difference i.e. a three-place map of the form

$$\begin{aligned} tf(x)+(1-t)f(y)-f(tx+(1-t)y). \end{aligned}$$

We give a general solution of a functional equation associated with this problem.

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

    Andrzej Olbryś

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  1. Andrzej Olbryś
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Correspondence to Andrzej Olbryś.

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Olbryś, A. Characterization of affine differences and related forms. Aequat. Math. 96, 1303–1314 (2022). https://doi.org/10.1007/s00010-022-00887-1

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  • DOI: https://doi.org/10.1007/s00010-022-00887-1

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