# Level sets of continuous functions increasing with respect to each variable

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

- Volume: 25, Issue: 1, page 19-26
- ISSN: 1509-9407

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topKatarzyna Sajbura. "Level sets of continuous functions increasing with respect to each variable." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 25.1 (2005): 19-26. <http://eudml.org/doc/271441>.

@article{KatarzynaSajbura2005,

abstract = {
We are going to prove that level sets of continuous functions increasing with respect to each variable are arcwise connected (Theorem 3) and characterize those of them which are arcs (Theorem 2). In [3], we will apply the second result to the classical linear functional equation
φ∘f = gφ + h
(cf., for instance, [1] and [2]) in a case not studied yet, where f is given as a pair of means, that is so-called mean-type mapping.
},

author = {Katarzyna Sajbura},

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

keywords = {level set; continuous function; function increasing with respect to each variable; arcwise connectedness; arcwise connected level sets},

language = {eng},

number = {1},

pages = {19-26},

title = {Level sets of continuous functions increasing with respect to each variable},

url = {http://eudml.org/doc/271441},

volume = {25},

year = {2005},

}

TY - JOUR

AU - Katarzyna Sajbura

TI - Level sets of continuous functions increasing with respect to each variable

JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization

PY - 2005

VL - 25

IS - 1

SP - 19

EP - 26

AB -
We are going to prove that level sets of continuous functions increasing with respect to each variable are arcwise connected (Theorem 3) and characterize those of them which are arcs (Theorem 2). In [3], we will apply the second result to the classical linear functional equation
φ∘f = gφ + h
(cf., for instance, [1] and [2]) in a case not studied yet, where f is given as a pair of means, that is so-called mean-type mapping.

LA - eng

KW - level set; continuous function; function increasing with respect to each variable; arcwise connectedness; arcwise connected level sets

UR - http://eudml.org/doc/271441

ER -

## References

top- [1] M. Kuczma, Functional equations in a single variable, Monografie Mat. 46, Polish Scientific Publishers, Warszawa 1968. Zbl0196.16403
- [2] M. Kuczma, B. Choczewski and R. Ger, Iterative functional equations, Encyclopedia of mathematics and its applications 32, Cambridge University Press, Cambridge, 1990. Zbl0703.39005
- [3] K. Sajbura, On a linear functional equation with a mean-type mapping having no fixed points, Discuss. Math. DICO 25 (2005), 27-46. Zbl1111.39019

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