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The aim of this article is to investigate the neutrosophic Nörlund ℐ-statistically convergent sequence space. We present some neutrosophic normed spaces (NNSs) in Nörlund convergent spaces. In addition, we also examine various topological and algebraic properties of these convergent sequence spaces. Theorems are proved in light of the NNS theory approach. Results are obtained via different perspectives and new examples are produced to justify the counterparts and show the existence of the introduced notions. The results established in this research work supply an exhaustive foundation in NNS and make a significant contribution to the theoretical development of NNS in the literature. The original aspect of this study is the first wholly up-to-date and thorough examination of the features and implementation of neutrosophic Nörlund ℐ-statistically convergent sequences in NNS, based upon the standard definition.

This paper aims to investigate new coincidence point theorems for self‐maps under an extended rational contraction. Our approach uses the p‐adic distance in partially ordered ultrametric spaces. Furthermore, to illustrate our major discoveries, we give a comprehensive numerical analysis. This study expands on prior research in partially ordered ultrametric spaces to provide a more comprehensive understanding of such spaces using rational contraction. [ABSTRACT FROM AUTHOR]

This research paper aims to introduce the concept of lacunary ideal Cauchy sequences of fuzzy variables in a credibility space. We establish the interrelationships between this notion with lacunary ideal convergent sequences in the same structure from several aspects of credibility. Furthermore, we explore the concepts of strongly lacunary Cauchy, strongly ℐ -lacunary Cauchy, and strongly ℐ ∗ -lacunary Cauchy sequences of fuzzy variables within the context of credibility. We also examine the interconnections between these concepts and analyze their relationships. [ABSTRACT FROM AUTHOR]

The primary objective of this study is to introduce the notion of ideal convergence in quaternion-valued generalized metric spaces. We define I-convergence and I*-convergence in these spaces and establish their equivalence through the definition of property (AP). Furthermore, we introduce Z-Cauchy and I*-Cauchy sequences, adapting classically theorems to suit quaternion-valued generalized metric spaces. We also present I-statistical convergence, I-lacunary statistical convergence, strong I-Cesàro summability, strong I-lacunary summability, [V, λ] (Z)-summability, and I-λ-statistically convergencein quaternion valued generalized metric spaces, along with their associated properties. [ABSTRACT FROM AUTHOR]

We present and explore the concept of a quaternion-valued g-metric space with specific foundational properties related to convergence in this study. The main goal of this study is to introduce γ-statistically convergent sequences and γ-statistically g-Cauchy sequences, examining their properties within quaternion-valued g-metric spaces. The research also includes discussions on natural inclusion theorems relevant to these concepts. [ABSTRACT FROM AUTHOR]

In this study, we present statistical convergence, statistical limit points, and statistical cluster points of double sequences in neutrosophic fuzzy G-metric space with order q, extending the notion of neutrosophic fuzzy metric space. We support our assertions with relevant theorems and elucidate them through illustrative examples. Following the establishment of statistical convergence and the scrutiny of its properties within these spaces, we explore the concepts of lacunary statistical convergence and strongly lacunary convergence of double sequences, while also investigating the relationships among them. [ABSTRACT FROM AUTHOR]

In this research article, we introduce ℐ {\mathcal{I}} -statistically pre-Cauchy sequences of complex uncertain variables in five different aspects of uncertainty, namely: in mean, in measure, in distribution, in almost sure, and in uniformly almost sure. We also explore the connection between ℐ {\mathcal{I}} -statistically pre-Cauchy sequences and ℐ {\mathcal{I}} -statistically convergent sequences using complex uncertain variables. Additionally, we initiate the study of ℐ {\mathcal{I}} -statistically pre-Cauchy sequences of complex uncertain variables through Orlicz functions. [ABSTRACT FROM AUTHOR]

The research paper primarily focuses to extend the concepts of strongly almost convergence and statistically almost convergence by incorporating the concept of λ-convergence for fuzzy variable sequences. Additionally, we aim to introduce new sequence spaces that are associated with the newly introduced conceptions in terms of an Orlicz mapping for these sequences. Furthermore, our goal is to propose and establish inclusion relations within these sequence spaces. [ABSTRACT FROM AUTHOR]

In this paper, we expand upon different concepts of convergence, including convergence in distribution, in the mean, and in measure, while also exploring uniform almost sure convergence of uncertain double sequences of fuzzy numbers in statistical context. Additionally, we present intriguing findings concerning these convergence concepts. [ABSTRACT FROM AUTHOR]

In this paper, some existing theories on convergence of sequences in fuzzy cone normed space (FCNS in short) are extended to lacunary ideal convergence in FCNS. An original concept, named lacunary convergence of sequence in FCNS, is investigated. Also, lacunary l-limit points and lacunary l-cluster points of sequences in FCNS are examined. Furthermore, lacunary Cauchy and lacunary l-Cauchy sequences in FCNS are presented and relationships between them are studied. [ABSTRACT FROM AUTHOR]

The aim of this paper is to investigate the intuitionistic Nörlund ℐ 2 -statistically convergent sequence space. We present some intuitionistic fuzzy normed spaces (IFNS) in Nörlund convergent spaces. Moreover, we also put forward several topological and algebraic properties of these convergent sequence spaces. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the concepts of deferred statistical convergence of order αβ and strongly s-deferred Cesaro summability of order αβ for fuzzy variable sequences in credibility space. Furthermore, the conditions of deferred statistical convergence almost surely of order αβ, deferred statistical convergence in credibility of order αβ, deferred statistical convergence in mean of order αβ, deferred statistical convergence in distribution of order αβ, and deferred statistical convergence uniformly almost surely of order αβ of fuzzy variable sequences have been examined. We have proved relations between these notions. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of rough Istatistical ϕ-convergence of real numbers as a generalization of rough statistical convergence as well as I-statistical ϕ-convergence. We study some of its fundamental properties. We obtain some results for rough I-statistical ϕ-convergence by introducing the rough Istatistical-ϕ limit set. So our main objective is to find out the different behaviour of the new convergence concept based on rough I-statistical-ϕ limit set. [ABSTRACT FROM AUTHOR]

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In this paper, we define g-convergence and g-Cauchy of double sequences in g-metric spaces. Also we prove that g-limit is unique and every g-convergent double sequence is a g-Cauchy sequence. Additionally g-statistical convergence of double sequences is introduced and the theorem giving the relationship between statistical convergence and strongly Cesáro summability in a g-metric space is demonstrated. Further, we put forward the notations of g-lacunary statistical convergence and g-strongly lacunary convergence of double sequences and we also present some inclusion theorems. [ABSTRACT FROM AUTHOR]

In this paper, we put forward rough statistical φ-convergence of difference sequences as a generalization of rough statistical convergence as well as statistical φ-convergence. We study some of its fundamental properties. We obtain some results for rough statistical φ-convergence for difference double sequences by introducing the rough statistical-φ limit set. So our main objective is to find out the different behaviour of the new convergence concept based on rough statistical-φ limit set. [ABSTRACT FROM AUTHOR]