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Random Stability of a Functional Equation Related to An Inner Product Space

Journal Name:

  • European Journal of Pure and Applied Mathematics

Publication Year:

  • 2012

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Abstract (2. Language): 
In [14], Th.M. Rassias introduced the following equality Xn i, j=1 kxi − x jk2 = 2n Xn i=1 kxik2, Xn i=1 xi = 0 for a fixed integer n ≥ 3. For a mapping f : X → Y , where X is a vector space and Y is a complete random normed space, we consider the following functional equation Xn i, j=1 f (xi − x j) = 2n Xn i=1 f (xi) (1) for all x1, . . . , xn ∈ X with Pn i=1 xi = 0. In this paper, we prove the Hyers-Ulam stability of the functional equation (1) related to an inner product space.
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  • English

REFERENCES

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