Hyers-Ulam-Rassias stability of approximate isometries on restricted domains
来源期刊:中南大学学报(英文版)2002年第4期
论文作者:XIANG Shu-huang
文章页码:289 - 292
Key words:Hyers-Ulam-Rassias stability; isometry; uniformly convex space; Hilbert space
Abstract: Let X and Y be real Banach spaces. The stability of Hyers-Ulam-Rassias approximate isometries on restricted domains S( unbounded or bounded ) for into mapping f:S→Ysatisfying ‖f(x)-f(y)‖-‖x-y‖ ≤ε(x,y) for allx,y∈Sis studied in case that the target spaceYis uniformly convex Banach space of the modulus of convexity of power type q≥2 orY is the Lq(Ω,∑,μ) (1p+‖y‖p or(x,y)=‖x-y‖p for p≠1 is investigated.