On the stability of an n-dimensional quadratic and additive functional equation
نویسندگان
چکیده
منابع مشابه
Stability of an n-Dimensional Mixed-Type Additive and Quadratic Functional Equation in Random Normed Spaces
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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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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Katsaras 1 defined a fuzzy norm on a vector space to construct a fuzzy vector topological structure on the space. Some mathematicians have defined fuzzy norms on a vector space from various points of view 2–4 . In particular, Bag and Samanta 5 , following Cheng and Mordeson 6 , gave an idea of fuzzy norm in such a manner that the corresponding fuzzy metric is of Kramosil and Michálek type 7 . T...
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ژورنال
عنوان ژورنال: Mathematical Inequalities & Applications
سال: 2006
ISSN: 1331-4343
DOI: 10.7153/mia-09-16