Hyers-Ulam-Rassias stability of approximate isometries on restricted domains

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ÂÛÎÄ×÷ÕߣºXIANG Shu-huang

ÎÄÕÂÒ³Â룺289 - 292

Key words£ºHyers-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¡úYsatisfying ¡¬f(x)-f(y)¡¬-¡¬x-y¡¬ ¡Ü¦Å¦¼(x,y) for allx,y¡ÊSis studied in case that the target spaceYis uniformly convex Banach space of the modulus of convexity of power type q¡Ý2 orY is the L^q(¦¸,¡Æ,¦Ì) (1p+¡¬y¡¬^p or¦¼(x,y)=¡¬x-y¡¬^p for p¡Ù1 is investigated.