LATTICTIC RANDOM STABILITY OF AN ADDITIVE-QUADRATIC FUNCTIONAL EQUATION BY FIXED POINT METHOD

摘要

In [39], Th.M. Rassias proved that the norm defined over a real vector space V is induced by an inner product if and only if for a fixed positive integer l 2l‖1/2l 2lΣi=1xi‖~2+2lΣi=1‖xi-2/2l 2lΣj=1xj‖~2=2lΣi=1‖xi‖~2 holds for all x1, • • • , x2l ∈ V. For the above equality, we can define the following functional equation 2lf(1/2l 2lΣi=1xi)+ 2lΣi=1f(xi-2/2l 2lΣj=1xj)= 2lΣi=1f(xi).(1)Using the fixed point method, we prove the generalized Hyers-Ulam stability of the functional equation (1) in complete lattictic random normed spaces.