Weakly convergent sequences 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.

We introduce double ? ?-statistically convergent sequences and double ? ?- statistically Cauchy sequences in the fuzzy normed spaces. We study [V,? ?] and [C,1]-summabilities for double sequences. In addition, we obtain the relation between these concepts and ? ?-statistically convergence.

The primary objective of this study is to introduce the concepts of $I_2$-deferred Cesàro summability and $I_2-$ deferred statistical convergence for double sequences in fuzzy normed spaces (FNS). Furthermore, the aim is to explore the connections between these concepts and subsequently establish several theorems pertaining to the notion of $I_2$-deferred statistical convergence in FNS for double sequences. We further define $I_2$-deferred statistical limit points and $I_2$-deferred statistical cluster points of a sequence within FNS and explore the relationships among these concepts.

In this paper, we delve into the exploration of ideal convergence within the framework of triple sequences on L -fuzzy normed spaces. Our primary focus is to establish a comprehensive characterization of ideal convergence for these triple sequences, particularly in relation to their convergence in the classical sense. Through rigorous analysis, we demonstrate that the notion of ideal convergence, as developed in this context, exhibits a weaker form of convergence compared to the traditional convergence criteria applied to triple sequences in L - fuzzy normed spaces. This weaker form of convergence, while more generalized, retains significant applicability and provides a broader understanding of the behavior of sequences within these structured spaces. The results presented herein offer new insights into the subtleties of sequence convergence in fuzzy normed spaces, paving the way for further advancements in this area of mathematical analysis.

In this paper, we introduce a new type of convergence for a sequence of function, namely, λ-statistically convergent sequences of functions in fuzzy 2-normed space, which is a natural generalization of convergence in fuzzy 2-normed space. In particular, we introduce the concepts of uniform λ-statistical convergence and pointwise λ-statistical convergence in the topology induced by fuzzy 2-normed spaces, and give some basic properties of these concepts.

We obtain the general solution of the following functional equation f(kx1+x2+???+xk)+f(x1+kx2+???+xk)+???+f(x1+x2+???+kxk)+f(x1)+ f(x2)+???+ f(xk)= 2kf(x1+ x2+???+xk), k ? 2. We establish the Hyers-Ulam-Rassias stability of the above functional equation in the fuzzy normed spaces. More precisely, we show under suitable conditions that a fuzzy q-almost affine mapping can be approximated by an affine mapping. Further, we determine the stability of same functional equation by using fixed point alternative method in fuzzy normed spaces.

We establish some stability results concerning the general cubic functional equation f(x + ky) - kf(x + y) + kf(x - y) - f(x - ky) = 2k(k2 - 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 approximately cubic mapping guarantees the completeness of the fuzzy normed spaces

Our goal in the present paper is to introduce a new type of fuzzy inner product space. After that, to illustrate this notion, some examples are introduced. Then we prove that that every fuzzy inner product space is a fuzzy normed space. We also prove that the cross product of two fuzzy inner spaces is again a fuzzy inner product space. Next, we prove that the fuzzy inner product is a non decreasing function. Finally, if U is a fuzzy complete fuzzy inner product space and D is a fuzzy closed subspace of U, then we prove that U can be written as a direct sum of D and the fuzzy orthogonal complement of D.

In this paper we give some definitions and properties of spectral theory in fuzzy Hilbert spaces also we introduce definitions Invariant under a linear operator on fuzzy normed spaces and reduced linear operator on fuzzy Hilbert spaces and we prove theorms related to eigenvalue and eigenvectors ,eigenspace in fuzzy normed , Invariant and reduced in fuzzy Hilbert spaces and show relationship between them.

Fuzzy bounded linear operators

The aim of this paper is to obtain several topological characteristics of fuzzy normed linear spaces. We study the vector topology induced by a fuzzy norm. The notion of Schauder basis is developed in fuzzy normed linear spaces.

In this article we define the notion of fuzzy normed linear space valued sequence space lFp (X), 1 ≤ p < ∞ in a fuzzy normed linear space X and discuss some of its properties like completeness, monotone, solidness, convergence free and symmetricity. Also we prove some inclusion results.

Finite dimensional fuzzy normed linear space

In this paper we will highlight some properties of fuzzy bounded sets in fuzzy normed linear spaces. More precisely, we will prove that any finite union or sum of fuzzy bounded sets is fuzzy bounded. We show that the closure of a fuzzy bounded set is also fuzzy bounded. We give a characterization for fuzzy bounded sets and finally we obtain that the Cartesian product of two fuzzy bounded sets is also fuzzy bounded.

In this paper, we use the denition of fuzzy normed spaces given by Bag and Samanta and the behaviors of solutions of the additive functional equation are described. The Hyers-Ulam stability problem of this equation is discussed and theorems concerning the Hyers-Ulam-Rassias stability of the equation are proved on fuzzy normed linear space.