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

Abstract EN

Th.

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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, ∑i=1n∥xi-(1/n)∑j=1nxj∥2=∑i=1n∥xi∥2-n∥(1/n)∑i=1nxi∥2 holds for all x1,…,xn∈X.

The aim of this paper is to extend the applications of the fixed point alternative method to provide a fuzzy stability for the functional equation ∑i=1nf(xi-(1/n)∑j=1nxj)=∑i=1nf(xi)-nf((1/n)∑i=1nxi) which is said to be a functional equation associated with inner product spaces.