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

Katarzyna Sajbura

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

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

Abstract

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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.

How to cite

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Katarzyna 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

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

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