# On the uniqueness of continuous solutions of functional equations

Annales Polonici Mathematici (1995)

- Volume: 60, Issue: 3, page 231-239
- ISSN: 0066-2216

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topBolesław Gaweł. "On the uniqueness of continuous solutions of functional equations." Annales Polonici Mathematici 60.3 (1995): 231-239. <http://eudml.org/doc/262466>.

@article{BolesławGaweł1995,

abstract = {
We consider the problem of the vanishing of non-negative continuous solutions ψ of the functional inequalities
(1) ψ(f(x)) ≤ β(x,ψ(x))
and
(2) α(x,ψ(x)) ≤ ψ(f(x)) ≤ β(x,ψ(x)),
where x varies in a fixed real interval I. As a consequence we obtain some results on the uniqueness of continuous solutions φ :I → Y of the equation
(3) φ(f(x)) = g(x,φ(x)),
where Y denotes an arbitrary metric space.
},

author = {Bolesław Gaweł},

journal = {Annales Polonici Mathematici},

keywords = {functional equation; functional inequality; periodic point; cycle; uniqueness; metric space; functional inequalities; continuous solutions; nonlinear iterative functional equation},

language = {eng},

number = {3},

pages = {231-239},

title = {On the uniqueness of continuous solutions of functional equations},

url = {http://eudml.org/doc/262466},

volume = {60},

year = {1995},

}

TY - JOUR

AU - Bolesław Gaweł

TI - On the uniqueness of continuous solutions of functional equations

JO - Annales Polonici Mathematici

PY - 1995

VL - 60

IS - 3

SP - 231

EP - 239

AB -
We consider the problem of the vanishing of non-negative continuous solutions ψ of the functional inequalities
(1) ψ(f(x)) ≤ β(x,ψ(x))
and
(2) α(x,ψ(x)) ≤ ψ(f(x)) ≤ β(x,ψ(x)),
where x varies in a fixed real interval I. As a consequence we obtain some results on the uniqueness of continuous solutions φ :I → Y of the equation
(3) φ(f(x)) = g(x,φ(x)),
where Y denotes an arbitrary metric space.

LA - eng

KW - functional equation; functional inequality; periodic point; cycle; uniqueness; metric space; functional inequalities; continuous solutions; nonlinear iterative functional equation

UR - http://eudml.org/doc/262466

ER -

## References

top- [1] B. Gaweł, A linear functional equation and its dynamics, in: European Conference on Iteration Theory, Batschuns, 1989, Ch. Mira et al. (eds.), World Scientific, 1991, 127-137. Zbl0991.39503
- [2] B. Gaweł, On the uniqueness of continuous solutions of an iterative functional inequality, in: European Conference on Iteration Theory, Lisbon, 1991, J. P. Lampreia et al. (eds.), World Sci., 1992, 126-135.
- [3] W. Jarczyk, Nonlinear functional equations and their Baire category properties, Aequationes Math. 31 (1986), 81-100. Zbl0608.39002
- [4] M. Krüppel, Ein Eindeutigkeitssatz für stetige Lösungen von Funktionalgleichungen, Publ. Math. Debrecen 27 (1980), 201-205. Zbl0463.39008
- [5] M. Kuczma, Functional Equations in a Single Variable, Monografie Mat. 46, PWN-Polish Scientific Publishers, 1968.
- [6] M. Kuczma, B. Choczewski and R. Ger, Iterative Functional Equations, Encyclopedia Math. Appl. 32, Cambridge University Press, 1990. Zbl0703.39005

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