摘要：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,∑𝑛𝑖=1‖𝑥𝑖∑−(1/𝑛)𝑛𝑗=1𝑥𝑗‖2=∑𝑛𝑖=1‖𝑥𝑖‖2∑−𝑛‖(1/𝑛)𝑛𝑖=1𝑥𝑖‖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 ∑𝑛𝑖=1𝑓(𝑥𝑖∑−(1/𝑛)𝑛𝑗=1𝑥𝑗∑)=𝑛𝑖=1𝑓(𝑥𝑖∑)−𝑛𝑓((1/𝑛)𝑛𝑖=1𝑥𝑖) which is said to be a functional equation associated with inner product spaces.
