The purpose of this article is to investigate lacunary ideal convergence sequences in neutrosophic normed space (NNS). Also, an original notion, named sequence NNS, defined. $% \mathcal{I}$-limit points and $\mathcal{I}$-cluster NNS have been examined. Furthermore, Cauchy $\mathcal{I}$-Cauchy are introduced some properties these notions studied.

The notion of ideal convergence is a process generalizing statistical which dependent on the idea $I$ subsets set positive integer numbers. In this study we also present concept for triple sequences in fuzzy metric spaces (FMS) manner George and Veeramani terms Cauchy sequence $I^{∗}$-Cauchy FMS their certain properties.

In this paper, we deal with the notion of fuzzy metric space (X,M,∗), or simply X, due to George and Veeramani. It is well known that such spaces, in general, are not completable also there exist p-Cauchy sequences which Cauchy. We prove if every sequence X Cauchy, then principal, observe converse false, general. Hence, introduce study a stronger concept than called strongly principal. Moreover...

The terminology and notation used in this paper are introduced in the following papers: [22], [3], [20], [9], [5], [12], [10], [11], [15], [2], [18], [4], [1], [21], [16], [17], [14], [13], [19], [6], [7], and [8]. For simplicity, we follow the rules: X denotes a complex unitary space, s1, s2, s3 denote sequences of X, R1 denotes a sequence of real numbers, C1, C2, C3 denote complex sequences, ...

We investigate the effect on Cauchy complete objects of the change of base 2-functor V-Cat → W-Cat induced by a two-sided enrichment V → W. We restrict our study to the case of locally partially ordered bases. The reversibility notion introduced in [Wal82] is extended to two-sided enrichments and Cauchy completion. We show that a reversible left adjoint two-sided enrichment F : V → W between lo...

and Applied Analysis 3 In order to prove that the sequence {xn} is a Cauchy sequence with respect to norm ‖·‖C, we introduce an equivalent norm and show that {xn} is a Cauchy sequence with respect to the new one. Basing on the condition H2 , we see that there are two positive constantsM and m such that m ≤ y t ≤ M for all t ∈ R. Define the new norm ‖ · ‖1 by ‖u‖1 sup { 1 y t ‖u t ‖E : t ∈ R } ,...

In this study, we introduce the notion of pointwise and uniform statistical convergence of double sequences of real-valued functions. We also give the relations between these convergences and pointwise,uniform convergence. Furthermore, we introduce the concept of statistically Cauchy sequence and study statistical analogue of convergence and Cauchy criterion for double sequences of real-valued ...