QUADRATIC FUNCTIONAL EQUATIONS ASSOCIATED WITH BOREL FUNCTIONS AND MODULE ACTIONS

Title & Authors
QUADRATIC FUNCTIONAL EQUATIONS ASSOCIATED WITH BOREL FUNCTIONS AND MODULE ACTIONS
Park, Won-Gil; Bae, Jae-Hyeong;

Abstract
For a Borel function $\small{{\psi}:\mathbb{R}{\times}\mathbb{R}{\rightarrow}\mathbb{R}}$ satisfying the functional equation $\small{\psi}$ (s + t, u + v) + $\small{\psi}$(s - t, u - v) = $\small{2\psi}$(s, u) + $\small{2\psi}$(t, v), we show that it satisfies the functional equation $\small{\psi}$(s, t) = s(s - t)$\small{\psi}$(1, 0) + $\small{st\psi}$(1, 1) + t(t - s)$\small{\psi}$(0, 1). Using this, we prove the stability of the functional equation f(ax + ay, bz + bw) + f(ax - ay, bz - bw) = 2abf(x, z) + 2abf(y,w) in Banach modules over a unital $\small{C^*}$-algebra.
Keywords
Language
English
Cited by
1.
APPROXIMATE BI-HOMOMORPHISMS AND BI-DERIVATIONS IN C*-TERNARY ALGEBRAS,;;

대한수학회보, 2010. vol.47. 1, pp.195-209
1.
APPROXIMATE BI-HOMOMORPHISMS AND BI-DERIVATIONS IN C*-TERNARY ALGEBRAS, Bulletin of the Korean Mathematical Society, 2010, 47, 1, 195
2.
CHARACTERIZATIONS OF REAL HYPERSURFACES OF TYPE A IN A COMPLEX SPACE FORM, Bulletin of the Korean Mathematical Society, 2010, 47, 1, 1
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