# Invariant graphs of functions for the mean-type mappings

ESAIM: Proceedings (2012)

- Volume: 36, page 209-216
- ISSN: 1270-900X

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topMatkowski, Janusz. Fournier-Prunaret, D., Gardini, L., and Reich, L., eds. " Invariant graphs of functions for the mean-type mappings ." ESAIM: Proceedings 36 (2012): 209-216. <http://eudml.org/doc/251195>.

@article{Matkowski2012,

abstract = {Let I be a real interval, J a subinterval of
I, p ≥ 2 an integer number, and
M1, ... , Mp : Ip → I
the continuous means. We consider the problem of invariance of the graphs of functions
ϕ : Jp−1 → I
with respect to the mean-type mapping
M = (M1, ... , Mp).Applying a result on the existence and uniqueness of an M -invariant mean
[7], we prove that if the graph of a continuous function
ϕ : Jp−1 → I
is M-invariant, then ϕ satisfies a simple functional
equation. As a conclusion we obtain a theorem which, in particular, allows to determine
all the continuous and decreasing in each variable functions ϕ of the
M-invariant graphs. This improves some recent results on invariant curves
[8] where the case p = 2 is considered.},

author = {Matkowski, Janusz},

editor = {Fournier-Prunaret, D., Gardini, L., Reich, L.},

journal = {ESAIM: Proceedings},

keywords = {mean; mean-type mapping; invariant mean; function of invariant graph; iteration; functional equation},

language = {eng},

month = {8},

pages = {209-216},

publisher = {EDP Sciences},

title = { Invariant graphs of functions for the mean-type mappings },

url = {http://eudml.org/doc/251195},

volume = {36},

year = {2012},

}

TY - JOUR

AU - Matkowski, Janusz

AU - Fournier-Prunaret, D.

AU - Gardini, L.

AU - Reich, L.

TI - Invariant graphs of functions for the mean-type mappings

JO - ESAIM: Proceedings

DA - 2012/8//

PB - EDP Sciences

VL - 36

SP - 209

EP - 216

AB - Let I be a real interval, J a subinterval of
I, p ≥ 2 an integer number, and
M1, ... , Mp : Ip → I
the continuous means. We consider the problem of invariance of the graphs of functions
ϕ : Jp−1 → I
with respect to the mean-type mapping
M = (M1, ... , Mp).Applying a result on the existence and uniqueness of an M -invariant mean
[7], we prove that if the graph of a continuous function
ϕ : Jp−1 → I
is M-invariant, then ϕ satisfies a simple functional
equation. As a conclusion we obtain a theorem which, in particular, allows to determine
all the continuous and decreasing in each variable functions ϕ of the
M-invariant graphs. This improves some recent results on invariant curves
[8] where the case p = 2 is considered.

LA - eng

KW - mean; mean-type mapping; invariant mean; function of invariant graph; iteration; functional equation

UR - http://eudml.org/doc/251195

ER -

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