Iteration groups, commuting functions and simultaneous systems of linear functional equations

• Autorzy: Matkowski J.
• Języki publikacji: EN

Abstrakty

EN

Let (ƒt)t∈R be a measurable iteration group on an open interval I. Under some conditions, we prove that the inequalies g o ƒa ≤ ƒa o g and g o ƒb ≤ ƒb o g for some a, b ∈ R imply that g must belong to the iteration group. Some weak conditions under which two iteration groups have to consist of the same elements are given. An extension theorem of a local solution of a simultaneous system of iterative linear functional equations is presented and applied to prove that, under some conditions, if a function g commutes in a neighbourhood of ƒ with two suitably chosen elements ƒa and ƒb of an iteration group of ƒ then, in this neighbourhood, g coincides with an element of the iteration group. Some weak conditions ensuring equality of iteration groups are considered.

Słowa kluczowe

EN

iteration group; commuting functions; functional equations; functional inequalities

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2008
• Tom: Vol. 28, no. 4
• Strony: 529--539
• Opis fizyczny: Bibliogr. 5 poz.

Twórcy

autor

Matkowski J.

• University of Zielona Góra, Institute of Mathematics, Computer Science and Econometry, ul. Podgórna 50, 65-246 Zielona Góra, Poland,

Bibliografia

• [1] D. Krassowska, J. Matkowski, A pair of linear functional inequalities and a characterization of Lp-norm, Ann. Polon. Math. 85 (2005) 1, 1–10.
• [2] M. Kuczma, Functional equations in a single variable, Monografie Mat. 46, Polish Scientific Publishers, Warsaw, 1968.
• [3] J. Matkowski, Cauchy functional equation on restricted domain and commuting functions, in Iteration Theory and Its Functional Equations, Proc., Schloss Hofen 1984, Springer Verlag 1163 (1985), 101–106.
• [4] J. Matkowski, On extension of solutions of a simultaneous system of linear functional equations (in peparation).
• [5] M.C. Zdun, Continuous and differentiable iteration groups, Prace Matematyczne, Silesian University, 1979.