Stability of Quadratic and Orthogonally Quadratic Functional Equations
stability of orthogonally functional equation
Abstract
In this study, the authors examine the generalized Hyers-Ulam stability of the following quadratic
functional equation
g(3x + 2y+z) + g(3x + 2y − z) + g(3x − 2y + z) + g(3x − 2y − z)
= 8[g(x + y) + g(x − y)] + 2[g(x + z) + g(x − z)] + 16g(x)
The preceding equation is changed and its generalized Hyers-Ulam stability for the following quadratic func-
tional equation
f(3x + 2y+z) + f(3x + 2y − z) + f(3x − 2y + z) + f(3x − 2y − z)
= 8[f(x + y) + f(x − y)] + 2[f(x + z) + f(x − z)] + 16f(x)
for any x, y, z ∈ X with x ⊥ y, y ⊥ z and z ⊥ x is studied in orthogonality space in the sense of R¨atz.
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References
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