Remarks on the stability of some quadratic functional equations

Tyt. z nagł.References p. 526-527.Dostępny również w formie drukowanej.ABSTRACT: Stability problems concerning the functional equations of the form f(2x + y) = 4ƒ(x) + ƒ(y) + ƒ(x + y) - ƒ(x - y), and ƒ(2x + y) + ƒ(2x -y) = 8ƒ(x) + 2ƒ(y) are investigated. We prove that if the norm of the difference between the LHS and the RHS of one of equations (1) or (2), calculated for a function g is say, dominated by a function φ in two variables having some standard properties then there exists a unique solution ƒ of this equation and the norm of the difference between g and ƒ is controlled by a function depending on φ. KEYWORDS: quadratic functional equations, stability