# On a linear functional equation with a mean-type mapping having no fixed points

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2005)

- Volume: 25, Issue: 1, page 27-46
- ISSN: 1509-9407

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topKatarzyna Sajbura. "On a linear functional equation with a mean-type mapping having no fixed points." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 25.1 (2005): 27-46. <http://eudml.org/doc/271543>.

@article{KatarzynaSajbura2005,

abstract = {
Our aim is to study continuous solutions φ of the classical linear iterative equation
φ(f(x,y)) = g(x,y)φ(x,y) + h(x,y),
where the given function f is defined as a pair of means. We are interested in the case when f has no fixed points. In turns out that in such a case continuous solutions of (1) depend on an arbitrary function.
},

author = {Katarzyna Sajbura},

journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},

keywords = {linear functional equation; iteration; mean; continuous solution; solution depending on an arbitrary function; linear iterative equation},

language = {eng},

number = {1},

pages = {27-46},

title = {On a linear functional equation with a mean-type mapping having no fixed points},

url = {http://eudml.org/doc/271543},

volume = {25},

year = {2005},

}

TY - JOUR

AU - Katarzyna Sajbura

TI - On a linear functional equation with a mean-type mapping having no fixed points

JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization

PY - 2005

VL - 25

IS - 1

SP - 27

EP - 46

AB -
Our aim is to study continuous solutions φ of the classical linear iterative equation
φ(f(x,y)) = g(x,y)φ(x,y) + h(x,y),
where the given function f is defined as a pair of means. We are interested in the case when f has no fixed points. In turns out that in such a case continuous solutions of (1) depend on an arbitrary function.

LA - eng

KW - linear functional equation; iteration; mean; continuous solution; solution depending on an arbitrary function; linear iterative equation

UR - http://eudml.org/doc/271543

ER -

## References

top- [1] M. Kuczma, Functional equations in a single variable, Monografie Mat. 46, Polish Scientific Publishers, Warszawa 1968. Zbl0196.16403
- [2] J. Matkowski, Invariant and complementary quasi-arithmetic means, Aequationes Math. 57 (1999), 87-107. Zbl0930.26014
- [3] J. Matkowski, Iterations of mean-type mappings and invariant means, Ann. Math. Sil. 13 (1999), 211-226. Zbl0954.26015
- [4] K. Sajbura, Level sets of continuous functions increasing with respect to each variable, Discuss. Math. DICO 25 (2005), 19-26. Zbl1170.26302