In this paper level-cut measures of noncompactness are introduced in standard fuzzy normed spaces and condensing operators are studied. Using the extensions of nonlinear compact operators, topological degree theory with respect to condensing operators is given in standard fuzzy normed spaces. As an application of degree theory, a fixed point theorem for condensing operators is presented. © 2009...

In this paper, we investigate the general solution and the generalized Hyers-Ulam stability of a new functional equation satisfied by $f(x) = x^{24}$, which is called quattuorvigintic functional equation in intuitionistic fuzzy normed spaces by using the fixed point method.These results can be regarded as an important extension of stability results corresponding to functional equations on norme...

Some new concepts of generating spaces of quasi-norm family are introduced and their linear topological structures are studied. These spaces are not necessarily locally convex. By virtue of some properties in these spaces, several Schauder-type fixed point theorems are proved, which include the corresponding theorems in locally convex spaces as their special cases. As applications, some new fix...

We establish some stability results concerning the general cubic functional equation f(x+ ky)− kf(x+ y) + kf(x− y)− f(x− ky) = 2k(k − 1)f(y) for fixed k ∈ N\{1} in the fuzzy normed spaces. More precisely, we show under some suitable conditions that an approximately cubic function can be approximated by a cubic mapping in a fuzzy sense and we establish that the existence of a solution for any ap...

In this paper, we introduce the notion of multi-fuzzy normed spaces and establish an asymptotic behavior of the quadratic functional equations in the setup of such spaces. We then investigate the superstability of strongly higher derivations in the framework of multi-fuzzy Banach algebras

In this paper, the definition of intuitionistic fuzzy normed linear space which is introduced in an earlier paper by R. Saadati et al. [15] is redefined and based on this revised definition we have studied completeness and connectedness of finite dimensional intuitionistic fuzzy normed linear spaces.

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...

In this paper we study some aspects of the topological structure of the weak fuzzy normed spaces and its relation with the topological vector spaces. We give characterizations of those topological vector spaces that are metrizable, locally bounded and normable in terms of weak fuzzy norms. Mathematics Subject Classification (2010): 54A40, 46S40, 54E35, 46A03, 46A16.