On the uniqueness of continuous solutions of functional equations

• Autorzy: Bolesław Gaweł
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

functional equation; functional inequality; periodic point; cycle

Kategorie tematyczne

• 26A18: Iteration

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1994-1995
• Tom: 60
• Numer: 3
• Strony: 231-239

Daty

wydano

1995

otrzymano

1993-10-04

poprawiono

1994-05-13

Twórcy

autor

Bolesław Gaweł

• Institute of Mathematics, Silesian University, Bankowa 14, 40-007 Katowice, Poland

Bibliografia

• [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.
• [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.
• [4] M. Krüppel, Ein Eindeutigkeitssatz für stetige Lösungen von Funktionalgleichungen, Publ. Math. Debrecen 27 (1980), 201-205.
• [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.