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

M‎. ‎Eshaghi Gordji | Zendy; H. Khodaei | Zendy

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

Author(s) -

M‎. ‎Eshaghi Gordji,

H. Khodaei

Publication year - 2010

Publication title -

discrete dynamics in nature and society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.264

H-Index - 39

eISSN - 1607-887X

pISSN - 1026-0226

DOI - 10.1155/2010/140767

Subject(s) - mathematics , inner product space , functional equation , fixed point , norm (philosophy) , fuzzy logic , product (mathematics) , fixed point theorem , fixed point iteration , integer (computer science) , space (punctuation) , stability (learning theory) , pure mathematics , mathematical analysis , computer science , differential equation , geometry , artificial intelligence , political science , law , programming language , machine learning , operating system

Th. M. Rassias (1984) proved that the norm defined over a real vector space is induced by an inner product if and only if for a fixed integer ≥2,∑=1‖∑−(1/)=1‖2=∑=1‖‖2∑−‖(1/)=1‖2 holds for all 1,…,∈. 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 ∑=1(∑−(1/)=1∑)==1(∑)−((1/)=1) which is said to be a functional equation associated with inner product spaces

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