منابع مشابه
Approximate mixed additive and quadratic functional in 2-Banach spaces
In the paper we establish the general solution of the function equation f(2x+y)+f(2x-y) = f(x+y)+f(x-y)+2f(2x)-2f(x) and investigate the Hyers-Ulam-Rassias stability of this equation in 2-Banach spaces.
متن کاملSuperstability of $m$-additive maps on complete non--Archimedean spaces
The stability problem of the functional equation was conjectured by Ulam and was solved by Hyers in the case of additive mapping. Baker et al. investigated the superstability of the functional equation from a vector space to real numbers. In this paper, we exhibit the superstability of $m$-additive maps on complete non--Archimedean spaces via a fixed point method raised by Diaz and Margolis.
متن کاملApproximation of an additive mapping in various normed spaces
In this paper, using the fixed point and direct methods, we prove the generalized Hyers-Ulam-Rassias stability of the following Cauchy-Jensen additive functional equation: begin{equation}label{main} fleft(frac{x+y+z}{2}right)+fleft(frac{x-y+z}{2}right)=f(x)+f(z)end{equation} in various normed spaces. The concept of Hyers-Ulam-Rassias stability originated from Th. M. Rassias’ stability theorem t...
متن کاملApproximate multi-additive mappings in 2-Banach spaces
A mapping $f:V^n longrightarrow W$, where $V$ is a commutative semigroup, $W$ is a linear space and $n$ is a positive integer, is called multi-additive if it is additive in each variable. In this paper we prove the Hyers-Ulam stability of multi-additive mappings in 2-Banach spaces. The corollaries from our main results correct some outcomes from [W.-G. Park, Approximate additive mappings i...
متن کاملFinitely additive representation of L spaces
Let λ̄ be any atomless and countably additive probability measure on the product space {0,1}N with the usual σ -algebra. Then there is a purely finitely additive probability measure λ on the power set of a countable subset T ⊂ T̄ such that Lp(λ̄) can be isometrically isomorphically embedded as a closed subspace of Lp(λ). The embedding is strict. It is also ‘canonical,’ in the sense that it maps si...
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ژورنال
عنوان ژورنال: Positivity
سال: 2014
ISSN: 1385-1292,1572-9281
DOI: 10.1007/s11117-014-0304-6