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We introduce three reasonable versions of fuzzy approximately additive functions in fuzzy normed spaces. More precisely, we show under some suitable conditions that an approximately additive function can be approximated by an additive mapping in a fuzzy sense.
We establish a generalized Hyers–Ulam–Rassias stability theorem in the fuzzy sense. In particular, we introduce the notion of fuzzy approximate Jensen mapping and prove that if a fuzzy approximate Jensen mapping is continuous at a point, then we can approximate it by an everywhere continuous Jensen mapping. As a fuzzy version of a theorem of Schwaiger, we… (More)
We approximate a fuzzy almost quadratic function by a quadratic function in a fuzzy sense. More precisely, we establish a fuzzy Hyers–Ulam–Rassias stability of the quadratic functional equation f (x + y) + f (x − y) = 2f (x) + 2f (y). Our result can be regarded as a generalization of the stability phenomenon in the framework of normed spaces. We also prove… (More)
In this paper we introduce a notion of a non-Archimedean fuzzy norm and study the stability of the Cauchy equation in the context of non-Archimedean fuzzy spaces in the spirit of Hyers–Ulam–Rassias–G˘ avru¸ta. As a corollary, the stability of the Jensen equation is established. We indeed present an interdisciplinary relation between the theory of fuzzy… (More)
We will define a notion for a quasi fuzzy p-normed space, then we use the fixed point alternative theorem to establish Hyers–Ulam– Rassias stability of the quartic functional equation where functions map a linear space into a complete quasi fuzzy p-normed space. Later, we will show that there exists a close relationship between the fuzzy continuity behavior… (More)
In this paper, we investigate a fuzzy version of stability for the functional equation 2f (x + y) + f (x − y) + f (y − x) − 3f (x) − f (−x) − 3f (y) − f (−y) = 0 in the sense of M. Mirmostafaee and M. S. Moslehian.
We will establish stability of Fréchet functional equation ∆ n x 1 ,...,xn f (y) = 0 in non-Archimedean normed spaces for some unbounded control function. Among some applications of our results, we will give a counterexample to show that the nature of stability in non-Archimedean normed spaces is different from one in classical normed spaces.
We will show that if X is a tree-complete subspace of ∞ , which contains c 0 , then it does not admit any weakly midpoint locally uniformly convex renorming. It follows that such a space has no equivalent Kadec renorming. 1. Introduction. It is known that ∞ has an equivalent strictly convex renorming ; however, by a result due to Lindenstrauss, it cannot… (More)