Stability of Mappings of Hyers-Ulam Type

a₁ Acad additive function Aequationes Math Amer approximately additive mappings assume Banach spaces bounded Cauchy Cauchy sequence consider continuous at zero continuous functions continuous solution convergent COROLLARY D. H. Hyers D.H.Hyers defined denote E₁ E₂ EE2 satisfies exists a unique f(ax function f G₁ Hence Hilbert space holds homogeneous functions homomorphisms Hyers-Ulam stability Hyers-Ulam Type Hadronic implies induction isometry Kraków Lemma linear functional equation linear mapping locally convex space mapping f Mappings of Hyers-Ulam Moreover normed space normed vector space obtain orthogonality equation Palm Harbor paper problem Proc prove quadratic function Rassias real Banach space real normed space real numbers result S. M. Ulam S.M.Ulam sequence Shanholt spaces and let Stability of Mappings Suppose Tabor Th.M.Rassias topological topological group Type Hadronic Press U.S.A. ISBN Ulam stability vector space whence απ