Quadratic--quartic functional equations in RN--spaces

Mathematics – Functional Analysis

Scientific paper

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11 pages

Scientific paper

In this paper, we obtain the general solution and the stability result for
the following functional equation in random normed spaces (in the sense of
Sherstnev) under arbitrary $t$-norms
$$f(2x+y)+f(2x-y)=4[f(x+y)+f(x-y)]+2[f(2x)-4f(x)]-6f(y).$$

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