The Fixed Point Method for Fuzzy Approximation of a Functional Equation Associated with Inner Product Spaces
نویسندگان
چکیده
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 ∑n j 1 xj‖ ∑n i 1 ‖xi‖ − n‖ 1/n ∑ni 1 xi‖ 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 ∑n i 1 f xi− 1/n ∑n j 1 xj ∑n i 1 f xi −nf 1/n ∑n i 1 xi which is said to be a functional equation associated with inner product spaces.
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