Geodesic
Mean values for vector valued functions and corresponding functional equations
Commentationes Mathematicae, Tome 53 (2013) no. 2, p. 355−369.

Voir la notice de l'article provenant de la source Annales Societatis Mathematicae Polonae Series

Although, in general, a straightforward generalization of the Lagrange mean value theorem for vector valued mappings fails to hold we will look for what can be salvaged in that situation. In particular, we deal with Sanderson's and McLeod's type results of that kind (see [9] and [7], respectively). Moreover, we examine mappings with a prescribed intermediate point in the spirit of the celebrated Acz\'el's theorem characterizing polynomials of degree at most 2 (cf. [1]).
DOI : 10.14708/cm.v53i2.796
Mots-clés : mean value theorems, quasi-arithmetic means, Gauss-iteration, characterization of quadratic polynomials 
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Roman Ger; Maciej Sablik. Mean values for vector valued functions and corresponding functional equations. Commentationes Mathematicae, Tome 53 (2013) no. 2, p.  355−369. doi : 10.14708/cm.v53i2.796. http://geodesic.mathdoc.fr/articles/10.14708/cm.v53i2.796/

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