Mean values for vector valued functions and corresponding functional equations

Roman Ger, and Maciej Sablik. "Mean values for vector valued functions and corresponding functional equations." Commentationes Mathematicae 53.2 (2013): null. <http://eudml.org/doc/292416>.

@article{RomanGer2013,
abstract = {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 Aczél’s theorem characterizing polynomials of degree at most 2 (cf. [1]).},
author = {Roman Ger, Maciej Sablik},
journal = {Commentationes Mathematicae},
keywords = {mean value theorems, quasi-arithmetic means, Gauss-iteration, characterization of quadratic polynomials},
language = {eng},
number = {2},
pages = {null},
title = {Mean values for vector valued functions and corresponding functional equations},
url = {http://eudml.org/doc/292416},
volume = {53},
year = {2013},
}

TY - JOUR
AU - Roman Ger
AU - Maciej Sablik
TI - Mean values for vector valued functions and corresponding functional equations
JO - Commentationes Mathematicae
PY - 2013
VL - 53
IS - 2
SP - null
AB - 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 Aczél’s theorem characterizing polynomials of degree at most 2 (cf. [1]).
LA - eng
KW - mean value theorems, quasi-arithmetic means, Gauss-iteration, characterization of quadratic polynomials
UR - http://eudml.org/doc/292416
ER -