Stability of Mappings of Hyers-Ulam Type

additive function Aequationes Math af(x approximate isometries approximately additive mappings arbitrary function assume Banach space bounded Cauchy Cauchy sequence consider continuous at zero continuous functions continuous solution convergent COROLLARY D. H. Hyers D.H.Hyers defined denote E₁ E1 E2 satisfies E₂ exists a unique function f Hence Hilbert space holds homogeneous functions homomorphisms Hyers-Ulam stability Hyers-Ulam Type Hadronic implies induction isometry Jensen-convex Kraków Lemma Let hypotheses H1 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 Poland positive number problem Proc prove quadratic function Rassias real normed space real numbers result S. M. Ulam S.M.Ulam semigroup sequence Shanholt Stability of Mappings Suppose Tabor Th.M.Rassias topological topological group Type Hadronic Press U.S.A. ISBN Ulam stability vector space whence Ει