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and Applied Analysis 3 is Cauchy. If each Cauchy sequence is convergent, then the fuzzy norm is said to be complete, and the fuzzy normed space is called a fuzzy Banach space. Let X,N be a fuzzy normed space and Y,N ′ a fuzzy Banach space. For a given mapping f : X → Y , we use the abbreviation Df ( x, y ) : f ( 2x y ) f ( 2x − y 2f x − fx y − fx − y − 2f(More)
A classical question in the theory of functional equations is “when is it true that a mapping, which approximately satisfies a functional equation, must be somehow close to an exact solution of the equation?” Such a problem, called a stability problem of the functional equation, was formulated by Ulam 1 in 1940. In the next year, Hyers 2 gave a partial(More)
tributed 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 stability problems for a functional equation f (ax + y) + af (x − y) − a 2 +3a 2 f (x) − a(a−1) 2 f (−x) − f (y) − af (−y) = 0 by using(More)