Hyers-Ulam stability of quadratic functional equations in paranormed spaces

Abstract

Lin [18, 19] introduced and investigated the following quadratic functional equations cf(Sigma(n)(i=1)x(i)) + Sigma(n)(j=2)f (Sigma(n)(i=1)x(i) - (n + c - 1)x(j)) (0.1) = (n + c - 1) (f(x(1)) + c Sigma(n)(i=2)f(x(i)) + Sigma(n)(i<j,j=3) (Sigma(n-1)(i=2)f(x(i) - x(j)))), Q(Sigma(n)(i=1)d(i)x(i)) + Sigma(1 <= i<j <= n) d(i)d(j)Q(x(i) - x(j)) = (Sigma(n)(i=1)d(i)) (Sigma(n)(i=1)d(i)Q(x(i))). (0.2) In this paper, we prove the Hyers-Ulam stability of the above quadratic functional equations in para-normed spaces.