The main purpose of this paper is to consider the t-best simultaneousapproximation in fuzzy normed spaces. We develop the theory of t-bestsimultaneous approximation in quotient spaces. Then, we discuss the relationshipin t-proximinality and t-Chebyshevity of a given space and its quotientspace.

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...

The object of this paper is to determine Hyers–Ulam–Rassias stability concerning the Jensen functional equation in intuitionistic fuzzy normed space (IFNS) by using the fixed point method. Further, we establish stability of the Cauchy functional equation in IFNS.

In this paper, we study lacunary statistical convergence in intuition-istic fuzzy normed space. We also introduce here a new concept, that is, statistical completeness and show that IFNS is statistically complete but not complete.

Normed Space [1, 2, §2]. A norm ‖·‖ on a linear space (U ,F) is a mapping ‖·‖ : U → [0,∞) that satisfies, for all u,v ∈ U , α ∈ F , 1. ‖u‖ = 0 ⇐⇒ u = 0. 2. ‖αu‖ = |α| ‖u‖. 3. Triangle inequality: ‖u+ v‖ ≤ ‖u‖+ ‖v‖. A norm defines a metric d(u,v) := ‖u− v‖ on U . A normed (linear) space (U , ‖·‖) is a linear space U with a norm ‖·‖ defined on it. • The norm is a continuous mapping of U into R+. ...

P.Kostyrko et al [10] introduced the concept of Iconvergence of sequence in metric space and studied some properties of such convergence. Since then many author have been studied these subject and obtained various results [29,30,31,32,?] Note that I-convergence is an interesting generalization of statistical convergence. The concept of 2-normed space was initially introduced by Gähler [7] as an...

The claim that follows, which I have called the nite-dimensional normed linear space theorem, essentially says that all such spaces are topologically R with the Euclidean norm. This means that in many cases the intuition we obtain in R,R, and R by imagining intervals, circles, and spheres, respectively, will carry over into not only higher dimension R but also any vector space that has nite dim...

This study considers four means of defining differential operators for extracting local aspects of shape in ill-specified environments: fuzzy differentiation as kernel smoothing; differentiation in the sense of weak or generalized derivatives; differentiation for fuzzy functions between normed spaces; and fuzzy differentiation for mappings between fuzzy manifolds. More consideration is given to...

Scalarization of the multiobjective programming problems with fuzzy coefficients using the embedding theorem and the concept of convex cone (ordering cone) is proposed in this paper. Since the set of all fuzzy numbers can be embedded into a normed space, this motivation naturally inspires us to invoke the scalarization techniques in vector optimization problems to evaluate the multiobjective pr...