Quaestiones Mathematicae

Log in or Register to get access to full text downloads.

Remember me or Register

DOWNLOAD FULL TEXT Open Access  DOWNLOAD FULL TEXT Subscription or Fee Access

Lipschitz stability of the K-quadratic functional equation

Abdellatif Chahbi, Iz-iddine EL-Fassi, Samir Kabbaj


Let N be the set of all positive integers, G an Abelian group with a metric d and E a normed space. For any f : G → E we define the k-quadratic difference of the function f by the formula Qk ƒ(x; y) := 2ƒ(x) + 2k2ƒ(y) - f(x + ky) - f(x - ky) for x; y ∈ G and k ∈ N. Under some assumptions about f and Qkƒ we prove that if Qkƒ is Lipschitz, then there exists a quadratic function K : G → E such that ƒ -K is Lipschitz with the same constant. Moreover, some results concerning the stability of the k-quadratic functional equation in the Lipschitz norms are presented. Mathematics Subject Classification (2010): Primary 39B82, 39B52.

Key words: k-quadratic functional equation, stability, Lipschitz space.
AJOL African Journals Online