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Hyers-Ulam stability of quadratic forms in 2-normed spaces

Park Won-Gil, Bae Jae-Hyeong

Demonstratio Mathematica

2019

Vol. 52, nr 1

496--502

In this paper, we obtain Hyers-Ulam stability of the functional equations f(x+y, z+w) + f(x-y, z-w) = 2f(x, z) + 2f(y, w), f(x+y, z-w) + f(x-y, z+w) = 2f(x, z) + 2f(y, w) and f(x+y, z-w) + f(x-y, z+w) = 2f(x, z) - 2f(y, w) in 2-Banach spaces. The quadratic forms ax2+bxy+cy2, ax2+by2 and axy are solutions of the above functional equations, respectively.