ON THE GENERALIZED HYERS-ULAM STABILITY OF QUARTIC MAPPINGS IN NON-ARCHIMEDEAN BANACH SPACES

Abstract

Let X, Y are linear space. In this paper, we prove the generalized Hyers-Ulam stability of the following quartic equation Sigma(n)(k=2) (Sigma(k)(i1=2i2) Sigma(k+1)(=i1+1) ... Sigma(n)(in-k+1=in-k+1)) f (Sigma(n)(i=1,i not equal i1,....,in-k+1) x(i) - Sigma(n-k+1)(r=1) x(ir)) + f (Sigma(n)(i=1) x(i)) =2(n-2) Sigma(1 <= i <= j <= n) (f(x(i) + x(j)) + f(x(i) - x(j))) - 2(n-5)(n-2) Sigma(n)(i=1) f(2x(i)) (n is an element of N, n >= 3) in non-Archimedean Banach spaces