Affiliation:
1. Department of Mathematics Education, College of Education , Mokwon University , Daejeon 35349 , Republic of Korea
2. Humanitas College , Kyung Hee University , Yongin 17104 , Republic of Korea
Abstract
Abstract
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 ax
2 + bxy + cy
2, ax
2 + by
2 and axy are solutions of the above functional equations, respectively.
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