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 solution of Ulam’s problem for the case of...

in this paper, we propose a new definition of intuitionistic fuzzyquasi-metric and pseudo-metric spaces based on intuitionistic fuzzy points. weprove some properties of intuitionistic fuzzy quasi- metric and pseudo-metricspaces, and show that every intuitionistic fuzzy pseudo-metric space is intuitionisticfuzzy regular and intuitionistic fuzzy completely normal and henceintuitionistic fuzzy nor...

In this paper we introduce the cone bounded linear mapping and demonstrate a proof to show that the cone norm is continuous. Among other things, we prove the open mapping theorem and the closed graph theorem in TVS-cone normed spaces. We also show that under some restrictions on the cone, two cone norms are equivalent if and only if the topologies induced by them are the same. In the sequel, we...

in this work, we introduce notion of connectedness on fuzzy soft topological spaces and present fundamentals properties. we also investigate effect to fuzzy soft connectedness. moreover, c_i-connectedness which plays an important role in fuzzy topological space extend to fuzzy soft topological spaces.

We define and study the concept of non-Archimedean intuitionistic fuzzy normed space by using the idea of t-norm and t-conorm. Furthermore, by using the non-Archimedean intuitionistic fuzzy normed space, we investigate the stability of various functional equations. That is, we determine some stability results concerning the Cauchy, Jensen and its Pexiderized functional equations in the framewor...

In this paper, we introduce difference double sequence spaces ${I_{2} }^{(\mu,\upsilon)}(M,\Delta)$ and ${I_{2}^{0}}^{(\mu,\upsilon)}(M,\Delta)$ in the intuitionistic fuzzy normed linear spaces. We also investigate some topological properties of these

In this article, we deal with dual spaces and the Hahn-Banach Theorem. At the first, we defined dual spaces of real linear spaces and proved related basic properties. Next, we defined dual spaces of real normed spaces. We formed the definitions based on dual spaces of real linear spaces. In addition, we proved properties of the norm about elements of dual spaces. For the proof we referred to de...

we consider the concept of fuzzy quasi-contractions initiated by '{c}iri'{c} in the setting of fuzzy metric spaces and establish fixed point theorems for quasi-contractive mappings and for fuzzy $mathcal{h}$-contractive mappings on m-complete fuzzy metric spaces in the sense of george and veeramani.the results are illustrated by a representative example.

Here we show that Lerner’s method of local mean oscillation gives a simple proof of theA2 conjecture for spaces of homogeneous type: that is, the linear dependence on the A2 norm for weighted L 2 Calderon-Zygmund operator estimates. In the Euclidean case, the result is due to Hytönen, and for geometrically doubling spaces, Nazarov, Rezinikov, and Volberg obtained the linear bound.

Fuzzy set theory and fuzzy logic are the convenient tools for handling uncertain, imprecise, or unmodeled data in intelligent decision-making systems. The utility of fuzzy logic in system controls domain is presented in the context of a mobile robot navigation control application. The Takagi-Sugeno controller is a fuzzy model capable of approximating a wide class of nonlinear systems by decompo...