Approximation of Mixed-Type Functional Equations in Menger PN-Spaces

M. Eshaghi Gordji, H. Khodaei, Y. W. Lee and G. H. Kim

Abstract and Applied Analysis, 2012, vol. 2012, 1-17

Abstract:

Let and be vector spaces. We show that a function with satisfies for all , if and only if there exist functions , and such that for all , where the function is symmetric for each fixed one variable and is additive for fixed two variables, is symmetric bi-additive, is additive and ( , ) for all . Furthermore, we solve the stability problem for a given function satisfying , in the Menger probabilistic normed spaces.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:392179

DOI: 10.1155/2012/392179

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