Fuzzy Normed Spaces Research Articles

Uniform boundedness principle in generalized fuzzy normed linear spaces

In the present work, firstly uniform boundedness principle (UBP) theorem is established in a generalized fuzzy normed space from which Banach–Steinhaus theorem in fuzzy settings is derived. An example of an incomplete fuzzy normed linear space is constructed by applying the UBP theorem. Finally relation between our result and the existing UBP theorem of Bag and Samanta is studied.

Fuzzy Stability Results of Finite Variable Additive Functional Equation: Direct and Fixed Point Methods

In this current work, we introduce the finite variable additive functional equation and we derive its solution. In fact, we investigate the Hyers–Ulam stability results for the finite variable additive functional equation in fuzzy normed space by two different approaches of direct and fixed point methods.

On mathcal{I}_{{theta}_{2}}-convergence in fuzzy normed spaces

In this study, first, lacunary convergence of double sequences is introduced in fuzzy normed spaces, and basic definitions and theorems about lacunary convergence for double sequences are given in fuzzy normed spaces. Then, we introduce the concept of lacunary ideal convergence of double sequences in fuzzy normed spaces, and the relation between lacunary convergence and lacunary ideal convergence is investigated for double sequences in fuzzy normed spaces. Finally, in fuzzy normed spaces, we give the concept of limit point and cluster point for double sequences, and the theorems related to these concepts are given.

Fuzzy Bounded Linear Operator in Fuzzy Normed Linear Spaces and its Fuzzy Compactness

In this paper, we first investigate the relationship between various notions of fuzzy boundedness of linear operators in fuzzy normed linear spaces. We also discuss the fuzzy boundedness of fuzzy compact operators. Furthermore, the spaces of fuzzy compact operators have been studied.

On some topological properties of intuitionistic $2$-fuzzy $n$-normed linear spaces

Motivated by the notion of $n$-norm due to Gähler, in this article we define the concept of intuitionistic $2$-fuzzy $n$-normed space in general setting of $t$-norm as a generalization of intuitionistic fuzzy normed space in the sense of Bag and Samanta. Further we define the notion of $\alpha$-$n$-norm corresponding to intuitionistic $2$-fuzzy $n$-norm. In addition, we discuss some basic properties of convergence and completeness for intuitionistic $2$-fuzzy $n$-normed spaces.

Quadratic (s1,s2)-functional inequality in fuzzy normed space

In this paper, we introduce and prove the Generalized Hyers-Ulam stability of Quadratic (s1,s2)-functional inequality in Fuzzy Normed space using the fixed point method.

Fuzzy Stability for Finite Variable Additive Functional Equation in Classical Methods

We examine the Ulam-Hyers stability of finite variable additive functional equation in fuzzy normed space using classical methods.

On m-expansive and m-contractives tuple operators in Hilbert spaces

In this paper, we investigate some stability results of the following finite dimensional additive functional equation where n is the positive integer with N − {0, 1, 2} and k is the only odd positive integers, in Fuzzy Normed space using direct and fixed point approaches.

HUR-approximation of an ELTA functional equation

The main goal of this paper is study of the Hyers-Ulam-Rassias stability (briefly HUR-approximation) of the following Euler-Lagrange type additive(briefly ELTA) functional equation ?nj=1f (1/2 ?1?i?n,i?j rixi- 1/2 rjxj) + ?ni=1 rif(xi)=nf (1/2 ?ni=1 rixi) where r1,..., rn ? R, ?ni=k rk?0, and ri,rj?0 for some 1? i < j ? n, in fuzzy normed spaces. The concept of HUR-approximation originated from Th. M. Rassias stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300.

On Fixed Point Theorem in Non-Archimedean Fuzzy Normed Spaces

Let (X, N) be a non-archimedean fuzzy normed space and (X, k.k), a non-archimedean normed space where X is a linear space over a linearly ordered non-archimedean field K with a non-archimedean valuation. We give a proof of the fixed point theorem in non-archimedean Fuzzy normed space.

On (λ,μ)- Zweier ideal convergence in intuitionistic fuzzy normed space

In this paper, we study and introduce a new type of convergence, namely (?,?)- Zweier convergence and (?,?)- Zweier ideal convergence of double sequences x = (xij) in intuitionistic fuzzy normed space (IFNS), where ? = (?n) and ?= (?m) are two non-decreasing sequences of positive real numbers such that each tending to infinity. Furthermore, we studied (?,?)- Zweier Cauchy and (?,?)- Zweier ideal Cauchy sequences on the said space and established a relation between them.

Continuous linear transformations on generalized fuzzy normed spaces

Continuous linear transformations on generalized fuzzy normed spaces

Some properties of fuzzy normed linear spaces and fuzzy Riesz bases

Some properties of fuzzy normed linear spaces and fuzzy Riesz bases

Diameter Approximate Best Proximity Pair in Fuzzy Normed Spaces

The main purpose of this paper is to study the approximate best proximity pair of cyclic maps and their diameter in fuzzy normed spaces defined by Bag and Samanta. First, approximate best point proximity points on fuzzy normed linear spaces are defined and four general lemmas are given regarding approximate fixed point and approximate best proximity pair of cyclic maps on fuzzy normed spaces. Using these results, we prove theorems for various types of well-known generalized contractions in fuzzy normed spaces. Also, we apply our results to get an application of approximate fixed point and approximate best proximity pair theorem of their diameter.

Intuitionistic fuzzy I-convergent Fibonacci difference sequence spaces

Fibonacci difference matrix was defined by Kara in his paper (Kara in J. Inequal. Appl. 2013:38 2013). Recently, Khan et al. (Adv. Differ. Equ. 2018:199, 2018) using the Fibonacci difference matrix F̂ and ideal convergence defined the notion of c_{0}^{I}(hat{F}), c^{I}(hat{F}) and l_{infty }^{I}(hat{F}). In this paper, we give the ideal convergence of Fibonacci difference sequence space in intuitionistic fuzzy normed space with respect to fuzzy norm (mu ,nu ). Moreover, we investigate some basic properties of the said spaces such as linearity, hausdorffness.

Fibonacci statistical convergence on intuitionistic fuzzy normed spaces

In this paper, we study the concept of Fibonacci statistical convergence on intuitionisitic fuzzy normed space. We define the Fibonacci statistically Cauchy sequences with respect to an intuitionisitic fuzzy normed space and introduce the Fibonacci statistical completenes with respect to an intuitionisitic fuzzy normed space.

Properties of a Complete Fuzzy Normed Algebra

The aim of this paper is to translate the basic properties of the classical complete normed algebra to the complete fuzzy normed algebra at this end a proof of multiplication fuzzy continuous is given. Also a proof of every fuzzy normed algebra without identity can be embedded into fuzzy normed algebra with identity and is an ideal in is given. Moreover the proof of the resolvent set of a non zero element in complete fuzzy normed space is equal to the set of complex numbers is given. Finally basic properties of the resolvent space of a complete fuzzy normed algebra is given.

Properties of a Complete Fuzzy Normed Algebra

The aim of this paper is to translate the basic properties of the classical complete normed algebra to the complete fuzzy normed algebra at this end a proof of multiplication fuzzy continuous is given. Also a proof of every fuzzy normed algebra without identity can be embedded into fuzzy normed algebra with identity and is an ideal in is given. Moreover the proof of the resolvent set of a non zero element in complete fuzzy normed space is equal to the set of complex numbers is given. Finally basic properties of the resolvent space of a complete fuzzy normed algebra is given.

An n-dimensional cubic functional equation and its Hyers–Ulam stability

In this article, we introduce and discuss the general solution of a new n-dimensional cubic functional equation. Furthermore, we establish the generalized Hyers–Ulam stability of this functional equation in fuzzy normed spaces using direct and fixed point approach.

Statistical convergence of order β in fuzzy normed linear spaces

Statistical convergence of order β in fuzzy normed linear spaces