Stability properties of monomial functions

• Autorzy: Budzik D.
• Języki publikacji: EN

Abstrakty

EN

A map M defined on a semigroup (group, Banach space etc.) S and taking values in an Abelian group is called monomial of degree at most n whenever Δⁿ_y M (x) = n!M (y), where Δⁿ_y stands for the n-th iterate of the usual difference operator Δ_y. We are looking for conditions upon a map F from S into a real normed linear space, controlled by ƒ in the sense that || n!F (y) - Δⁿ_y F(x) || ≤ n!ƒ (y) - Δⁿ_y ƒ(x), to be uniformly approximated by monomial mapping of degree at most n.

Słowa kluczowe

EN

stability; monomial function; control function; invariant means; selections of multifunctions

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
• Rocznik: 2002
• Tom: [Z] 42(2)
• Strony: 183--198
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Budzik D.

• Institute of Matematics and Computer Science, Pedagogical University of Częstochowa, Armii Krajowej 13/15, 42-201 Częstochowa, Poland
• Institute of Matematics, Silesian University, Bankowa 14, 40-007 Katowice, Poland

Bibliografia

• [1] R. Badora, R. Ger and Zsolt Páles, Additive selections and the stability of Cauchy functional equation, Bull. Austral. Math. Soc., (to appear).
• [2] R. Badora, Z. Páles and L. Székelyhidi, Monomial selections of set-valued maps, Aequationes Math. 58 (1999), 214-222.
• [3] D. Ž. Djoković, A representation theorem for (X1 - 1)(X2 - 1)... (Xn - 1) and its applications, Ann. Polon. Math. XXII (1969), 189-198.
• [4] R. Ger, On functional inequalities stemming from stability questions, International Series of Numerical Mathematics, Vol. 103 Birkhäuser Verlag Bassel, (1992), 227-240.
• [5] M. Kuczma, An introduction to the theory of functional equations and inequalities, Polish Scientific Publisher and Uniwersytet Śląski, Warszawa-Kraków-Katowice, (1985).
• [6] L. Székelyhidi, Convolution Type Functional Equations on Topological Abelian Groups, World Scientific, Singapore-New Jersey-London-Hong Kong, (1991).