The Fixed Point Method for Fuzzy Approximation of a Functional Equation Associated with Inner Product Spaces

Th. M. Rassias (1984) proved that the norm defined over a real vector space X is induced by an inner product if and only if for a fixed integer n >= 2 Sigma(n)(i=1) parallel to x(i) (1/n) Sigma(n)(j=1) parallel to x(j) parallel to(2) = Sigma(n)(i=1) parallel to x(i)parallel to(2) - n parallel to(1/n) Sigma(n)(i=1) x(i)parallel to(2) holds for all x(1),...x(n) is an element of X. The aim of this paper this is to extend the applications of the fixed point alternative method to provide a fuzzy stability for the functional equation Sigma(n)(i=1) f(x(i) -(1/n) Sigma(n)(j=1) x(j)) = Sigma(n)(i=1) f(x(i)) nf ((1/n) Sigma(n)(i=1) x(i)) which is said to be a functional equation associated with inner product spaces.