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초록· 키워드
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For a Borel function ψ : R × R → R satisfying the functional equation ψ(s + t, u + v) + ψ(s − t, u − v) = 2ψ(s, u) + 2ψ(t, v), we show that it satisfies the functional equation ψ(s, t) = s(s − t)ψ(1, 0) + stψ(1, 1) + t(t − s)ψ(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 C^(*)-algebra.
목차
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참고문헌 (7)
참고문헌 신청
F. Bonsall / 1973 / Complex Normed Algebras / Springer-Verlag
J. Acz´el / 1989 / Functional Equations in Several Variables / Cambridge Univ. Press
J.-H. Bae / 2007 / A functional equation originating from quadratic forms / J. Math. Anal. Appl. 326 (2) : 1142 ~ 1148
K. Davidson / 1996 / C?-Algebras by Example / American Mathematical Society
R. Kadison / 1985 / Means and convex combinations of unitary operators / Math. Scand 57 (2) : 249 ~ 266
J. Acz´el / 1989 / Functional Equations in Several Variables / Cambridge Univ. Press
J.-H. Bae / 2007 / A functional equation originating from quadratic forms / J. Math. Anal. Appl. 326 (2) : 1142 ~ 1148
K. Davidson / 1996 / C?-Algebras by Example / American Mathematical Society
R. Kadison / 1985 / Means and convex combinations of unitary operators / Math. Scand 57 (2) : 249 ~ 266
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