On the stability of a mixed $n$-dimensional quadratic functional equation
نویسندگان
چکیده
منابع مشابه
stability of the quadratic functional equation
In the present paper a solution of the generalizedquadratic functional equation$$f(kx+ y)+f(kx+sigma(y))=2k^{2}f(x)+2f(y),phantom{+} x,yin{E}$$ isgiven where $sigma$ is an involution of the normed space $E$ and$k$ is a fixed positive integer. Furthermore we investigate theHyers-Ulam-Rassias stability of the functional equation. TheHyers-Ulam stability on unbounded domains is also studied.Applic...
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distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract In this paper, we investigate the generalized Hyers-Ulam stability of a functional equation 1≤i,j≤n, i =j f (x i + x j) + f (x i − x j) = (n − 1) n i=1 3f (x i) + f (−x i) .
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In 1940, Ulam 1 gave a wide-ranging talk before a mathematical colloquium at the University of Wisconsin, in which he discussed a number of important unsolved problems. Among those was the following question concerning the stability of homomorphisms. Let G1 be a group, and let G2 be a metric group with a metric d ·, · . Given ε > 0, does there exist a δ > 0 such that if a function h : G1 → G2 s...
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in the present paper a solution of the generalizedquadratic functional equation$$f(kx+ y)+f(kx+sigma(y))=2k^{2}f(x)+2f(y),phantom{+} x,yin{e}$$ isgiven where $sigma$ is an involution of the normed space $e$ and$k$ is a fixed positive integer. furthermore we investigate thehyers-ulam-rassias stability of the functional equation. thehyers-ulam stability on unbounded domains is also studied.applic...
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ژورنال
عنوان ژورنال: Bulletin of the Belgian Mathematical Society - Simon Stevin
سال: 2008
ISSN: 1370-1444
DOI: 10.36045/bbms/1203692443