On functions with the Cauchy difference bounded by a functional

• Autorzy: Fechner W.
• Języki publikacji: EN

Abstrakty

EN

K. Baron and Z. Kominek [2] have studied the functional inequality f(x + y) - f(x) - f(y) is less than or equal [phi](x, y), x, y is an element of X, under the assumptions that X is a real linear space, (phi] is homogeneous with respect to the second variable and f satisfies certain regularity conditions. In particular, they have shown that [phi] is bilinear and symmetric and f has a representation of the form f(x) =1/2[phi](x,x) + L[x) for x is an element of X, where L is a linear function. The purpose of the present paper is to consider this functional inequality under different assumptions upon X, f and [phi). In particular we will give conditions which force biadditivity and symmetry of (pchi] and the representation f(x) =1/2[phi](x, x) - A(x) for x is an element of X, where A is a subadditive function.

Słowa kluczowe

EN

functional inequality; subadditive; quadratic and biadditive functionals

PL

nierówność funkcjonalna; subaddytywność

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2004
• Tom: Vol. 52, nr 3
• Strony: 265--271
• Opis fizyczny: Bibliogr. 4 poz.

Twórcy

autor

Fechner W.

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

Bibliografia

• [1] J. Aczél and J. Dhombres, Functional Equations in Several Variables, Encyclopedia Math. Appl. 31, Cambridge Univ. Press, Cambridge, 1989.
• [2] K. Baron and Z. Kominek, On functionals with the Cauchy difference bounded by a homogeneous functional, Bull. Polish Acad. Sci. Math. 51 (2003), 301-307.
• [3] M. Kuczma, B. Choczewski and R. Ger, Iterative Functional Equations, Encyclopedia Math. Appl. 32, Cambridge Univ. Press, Cambridge, 1990.
• [4] S. Rolewicz, ɸ-convex functions defined on metric spaces, Int. J. Math. Sci. 115 (2003), 2631-2652.