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Publications (119)
This paper explores the concepts of J-lacunary statistical limit points, J-lacunary statistical cluster points, and J-lacunary statistical Cauchy multiset sequences. Building upon previous work in the field, we investigate the relationships between J-lacunary statistical convergence and J *-lacunary statistical convergence in multiset sequences. Th...
The aim of this research article is to introduce the concept of strongly lacunary ideal convergence of sequences of fuzzy variables in a credibility space in different directions. We define strongly lacunary ideal convergence via credibility measure, credibility distribution function and expected value of the fuzzy variables which are indeed elemen...
This paper introduces the neutrosophic -statistical convergent difference sequence spaces defined through a modulus function. Additionally, we establish new topological spaces and examine various topological properties within these neutrosophic -statistical convergent difference sequence spaces.
The primary objective of this study is to introduce the notion of ideal convergence in quaternion-valued generalized metric spaces. We define Iconvergence and I ∗-convergence in these spaces and establish their equivalence through the definition of property (AP). Furthermore, we introduce I-Cauchy and I ∗-Cauchy sequences, adapting classically theo...
The aim of this paper is to introduce and investigate some neutrosophic fuzzy tribonacci ℐ-lacunary statistical convergent sequence spaces by utilizing the domain of regular tribonacci matrix A = ( a jk ). Morever, we also put forward various algebraic and topological features of these convergent sequence spaces and establish several interesting in...
The main purpose of this paper is to investigate different types of deferred convergent double sequences of fuzzy variables by using the notions of ideal convergence and μ-density in a given credibility space. We also establish a number of instances to illustrate the newly introduced notions in the same environment. In this study, we also present i...
This study focuses on developing and examining new definitions related to statistical convergence, modulus functions, and σ-density in 2-normed spaces. We explore various relationships between statistical f_σ-convergence, f_σ-statistical convergence, f_σ-statistically Cauchy sequences, f_σ-statistically bounded double sequences, and strongly f_(σ_s...
The central objective of this treatise is to introduce the concept (j,k)γ∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(j,k)^*_\gamma $$\end{document}–operation in f...
This paper defines the space S_(θ_uv)^α (Δ_s^j,f), encompassing all sequences that are (Δ_s^j,f)-lacunary statistically convergent of order α, utilizing an unbounded modulus function f, a double lacunary sequence θ_uv={(k_u,l_v )}, a generalized difference operator Δ_s^j, and a real number α ∈ (0,1]. Additionally, the space ω_(θ_uv)^α (Δ_s^j,f) is...
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 $I_2$-d...
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...
In the present paper, we set forth with the new notion of rough \(\mathcal {I}\)-deferred statistical convergence of order \(\alpha (0<\alpha \le 1)\) in gradual normed linear spaces (GNLS). We prove some fundamental features and implication relations of this convergence method. Also, we put forward the notion of gradual rough \(\mathcal {I}\)-defe...
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,...
This paper investigates the concept of deferred Nörlund I -statistical convergence in probability, mean of order r, distribution, and explores the relationships among these notions. We present a novel approach to deferred Nörlund I-statistical convergence, which allows for a deeper understanding of the convergence behavior in various contexts. We e...
This study introduces the concept of statistically pre-Cauchy sequences of fuzzy variables in five directions of credibility theory: almost surely, in measure, in mean, in distribution, and uniformly almost surely. However, the main focus is kept on statistically pre-Cauchy sequences in measure, in mean, and in distribution. Furthermore, a correlat...
In this manuscript, we introduce the concepts of strong N h p ð Þ-summability of order a and lacunary statistical convergence of order a for fuzzy variables in credibility space. We examine important connections between these ideas. The circumstances of lacunary statistical convergence almost surely (a.s.) of order a, lacunary statistical convergen...
In this study, we investigate the notions of ℐ 2-convergence almost surely (a.s.) and ℐ2-convergence a.s. of complex uncertain double sequences in an uncertainty space, and obtain some of their features and identify the relationships between them. In addition , we put forward the concepts of ℐ 2 and ℐ2-Cauchy sequence a.s. of complex uncertain doub...
This work explores the concepts of deferred Cesàro mean and deferred statistical convergence for double sequences in neutrosophic normed spaces (shortly NNS). We investigate several fundamental properties of these newly studied concepts. Additionally, we introduce the notion of deferred statistical Cauchy sequences and establish the equivalence bet...
In this paper, the S θ (∆) and N θ (∆) summabilities are used along with the notion of weakly unconditionally Cauchy series (in brief wuC series) to characterize a Banach space. We examine these two kinds of summabilities which are regular methods and we recall some features. Furthermore, we investigate the spaces S N θ (p ∆w p) and S S θ (p ∆w p)...
In the present article, we set forth with the new notion of rough λ−statistical convergence in the gradual normed linear spaces. We produce significant results that present several fundamental properties of this notion. We also introduce the notion of λ r st (G)−limit set and prove that it is convex, gradually closed, and plays an important role fo...
A novel approach combining the difference operator on sequence spaces and uncertainty theory has been utilized to establish a fresh class of lacunary convergent difference sequences involving complex uncertain variables in 2-normed spaces. This newly introduced class demonstrates remarkable properties related to lacunary convergence. Additionally,...
In this article, we delve into the notions of I2-statistical convergence and I2-lacunary statistical convergence for sequences in general metric spaces, specifically g metric spaces. We thoroughly explore these concepts within the realm of g-metric spaces.
This study introduces the concept of rough I*-statistical convergence in a normed linear space, extending the notion of rough I-statistical convergence. Furthermore, we propose the concept of rough IK-statistical convergence in a more comprehensive framework. We examine the properties related to these novel concepts and explore the interconnections...
In this research, we investigate a specific family of conoid surfaces within the three-dimensional Euclidean space E3. We consider the differential geometry of the family. We determine the curvatures of these particular surfaces. Moreover, we provide the necessary conditions for minimality within this framework. Additionally, we compute the Laplace...
This study focuses on exploring a distinct family of conoid surfaces in the three-dimensional Minkowski space L3. Our main objective is to delve into the differential geometry of this family, analyzing its curvatures in detail. Furthermore, we establish the essential conditions for achieving minimality within this specific framework. Additionally,...
In this research, we investigate multiple conceptions of convergence and deferred statistical convergence of order \(\beta ,\) \(\left(0<\beta \le 1\right)\) for fuzzy variable sequences within framework credibility theory. The idea of deferred statistical convergence of order \(\beta\) for fuzzy variable sequences such as the notions of convergenc...
In this manuscript, we introduce the concepts of strong \(N_{\theta }\left( p\right)\)-summability of order \(\alpha\) and lacunary statistical convergence of order \(\alpha\) for fuzzy variables in credibility space. We examine important connections between these ideas. The circumstances of lacunary statistical convergence almost surely (a.s.) of...
Considering soft computing, the Weierstrass data (??1/2, ?1/2) gives two different minimal surface equations and figures. By using hard computing, we give the family of minimal and spacelike maximal surfaces S(m,n) for natural numbers m and n in Euclidean and Minkowski 3-spaces E3, E2,1, respectively. We obtain the classes and degrees of surfaces S...
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-...
Fast [12] is credited with pioneering the field of statistical convergence. This topic has been researched in many spaces such as topological spaces, cone metric spaces, and so on (see, for example [19, 21]). A cone metric space was proposed by Huang and Zhang [17]. The primary distinction between a cone metric and a metric is that a cone metric is...
In the present article, we introduce the concepts of strongly asymptotically lacunary equivalence, asymptotically statistical equivalence, asymptotically lacunary statistical equivalence for sequences in gmetric spaces. We investigate some properties and relationships among this new concepts.
The aim of this article is to investigate the neutrosophic Nörlund-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 appr...
The aim of this paper is to investigate the intuitionistic Nörlund [Formula: see text]-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.
We investigate the rough statistical convergence of complex uncertain
triple sequences in this research. We show three forms of rough statistically convergent complex uncertain triple sequences and rough lambda3-statistical convergence in measure, as well as other fundamental features.
In the present article, we introduce the concepts of strongly asymptotically lacunary equivalence, asymptotically statistical equivalence , and asymptotically lacunary statistical equivalence for sequences in g-metric spaces. We investigate some properties and relationships among these new concepts.
In the present article, we set forth with the new notion of rough A—statistical convergence in the gradual normed linear spaces. We produce significant results that present several fundamental properties of this notion. We also introduce the notion of Arst(G)—limit set and prove that it is convex, gradually closed, and plays an important role for t...
The main aim of this investigation is to introduce rough I-statistical convergence in probabilistic n-normed spaces (briefly Pr-n-spaces). We establish some results on roughI-statistical convergence and also we introduce the notion of rough I-statistical limit set in Pr-n-spaces and discuss some topological aspects on this set. Moreover, we define...
In this paper, we present the ideal convergence of triple sequences for rough variables. Furthermore, sequence convergence plays an extremely important role in the fundamental theory of mathematics. This paper presents two types of ideal convergence of rough triple sequence: Convergence in trust and convergence in mean. Some mathematical properties...
The main goal of this article is to present the notion of Fibonacci I-convergence of sequences on intuitionistic fuzzy normed linear space. To accomplish this goal, we mainly investigate some fundamental properties of the newly introduced notion. Then, we examine the Fibonacci I-Cauchy sequences and Fibonacci I completeness in the construction of a...
In the present article, we set forth with the new notion of rough statistical convergence in the gradual normed linear spaces (GNLS). We produce significant results that present several fundamental properties of this notion. We also introduce the \(st^{r}({\mathcal {G}})\)-limit set and prove that it is convex, gradually closed, and plays an import...
In this paper, we present the notions of lacunary statistically convergent
sequence for fuzzy variables, lacunary statistically Cauchy sequence in credibility space, and present a kind of lacunary statistical completeness for credibility space. Also, we present lacunary strong convergence concepts of sequences of fuzzy variables of different types.
In his paper, within frame work credibility theory, we examine several notions of convergence and statistical convergence of fuzzy variable sequences. The convergence of fuzzy variable sequences such i is the notion of convergence incredibility, convergence in distribution, convergence in mean,
and convergence uniformly virtually certainly via post...
In this note, we investigate some problems concerning the set of I_3I 3–\lambdaλ-statistical cluster points of triple sequences via ideals in finite dimensional spaces, and some of its properties in finite dimensional Banach spaces are proved.
The aim of this paper is to we examine the notion of gradually rough I_((λ,μ) )-statistical convergence of double sequences in gradual normed linear spaces (GNLS). In addition, we define the concept of gradually rough I_((λ,μ) )-statistical limit set of double sequences and obtain some algebraic and topological features of this set. Theorems are pr...
The intent of this paper is to investigate the intuitionistic Nörlund [Formula: see text]-lacunary 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.
The purpose of this article is to research the concept of Fibonacci lacunary ideal convergence of double sequences in intuitionistic fuzzy normed linear spaces (IFNS). Additionally, a new concept, called Fibonacci lacunary convergence, is examined. Also, Fibonacci lacunary I₂-limit points and Fibonacci lacunary I₂-cluster points for double sequence...
Kitap içerisinde, 3-boyutlu Euclidean uzayında Richmond minimal yüzeyler ailesinin parametrik denklemleri, Weierstrass-Enneper gösterim formülü yardımıyla elde edilmiş ve Gauss dönüşümleri hesaplanarak verilmiştir. Bu yüzeyler üzerinde eliminasyon (yok etme) metotları uygulanarak genelleştirilmiş indirgenemez cebirsel Richmond minimal yüzeyler aile...
degree number of Richmond's algebraic surface Q_{2}(x,y,z)=0 in cartesian coordinates is of 30.
class number of Richmond's algebraic surface Q^_{3}(a,b,c)=0 in inhomogeneous tangential coordinates is of 56.
In the present paper we introduce and study Orlicz lacunary convergent triple sequences over n-normed spaces. We make an effort to present the notion of $g_{3}$-ideal convergence in triple sequence spaces. We examine some topological and algebraic features of new formed sequence spaces. Some inclusion relations are obtained in this paper. Finally,...
Richmond's minimal surfaces family
class number of Richmond's algebraic surface Q^_{4}(a,b,c)=0 in inhomogeneous tangential coordinates is of 90.
In this paper, we introduce the concepts of $\mathcal{I}$-invariant arithmetic convergence, $\mathcal{I}^{\ast }$-invariant arithmetic convergence, strongly $q$-invariant arithmetic convergence for real sequences, and give some inclusion relations.
In this paper, we present the notions of statistically convergent sequence for fuzzy variables, statistically Cauchy sequence in credibility space, and present a kind of statistical completeness for credibility space. Furthermore, the conditions of statistical convergence almost surely (a.s.), statistical convergence in credibility, statistical con...
In this paper, our aim is to introduce new notions, namely, Wijsman asymptotically $\mathcal{I}_{2}$-statistical equivalence of weight $g$, Wijsman strongly asymptotically $\mathcal{I}_{2}$-lacunary equivalence of weight $g$ and Wijsman asymptotically $\mathcal{I}_{2}$-lacunary statistical equivalence of weight $g$ of double set sequences. We mainl...
We introduce the real minimal surfaces family by using the Weierstrass data (ζ−m,ζm) for ζ∈C, m∈Z≥2, then compute the irreducible algebraic surfaces of the surfaces family in three-dimensional Euclidean space E3. In addition, we propose that family has a degree number (resp., class number) 2m(m+1) in the cartesian coordinates x,y,z (resp., in the i...
The aim of this article is to investigate triple $\Delta $-statistical convergent sequences in a neutrosophic normed space (NNS). Also, we examine the notions of $\Delta $-statistical limit points and $\Delta $-statistical cluster points and prove their important features.
In this paper, some existing theories on convergence of fuzzy number sequences are extended to I2-statistical convergence of fuzzy number sequence. Also, we broaden the notions of I-statistical limit points and I-statistical cluster points of a sequence of fuzzy numbers to I2-statistical limit points and I2-statistical cluster points of a double se...
In this study, we investigate the notions of the Wijsman ℐ2-statistical convergence, Wijsman ℐ2-lacunary statistical convergence, Wijsman strongly ℐ2-lacunary convergence, and Wijsman strongly ℐ2-Cesàro convergence of double sequence of sets in the intuitionistic fuzzy metric spaces (briefly, IFMS). Also, we give the notions of Wijsman strongly ℐ2∗...
In this paper, we introduce the concept of I₂-lacunary statistical convergence and strongly I₂-lacunary convergence with respect to the intuitionistic fuzzy norm (μ,v), investigate their relationship, and make some observations about these classes. We mainly examine the relation between these two new methods and the relation between I₂-statistical...
Statistical convergence of sequences has been studied in neutrosophic normed spaces (NNS) by Kirişci and Şimşek [39]. Ideal convergence is more general than statistical convergence for sequences. This has motivated us to study the ideal convergence in NNS. In this paper, we study the concept of ideal convergence and ideal Cauchy for sequences in NN...
We consider a two parameter family of Henneberg-type minimal surfaces Hm,n using the Weierstrass representation in the four dimensional Euclidean space E4 . An invariant linear map of Weingarten type in the tangent space of the Henneberg-type minimal surface H4,2 which generates two invariants κκ and ϰϰ, is characterized by ϰ2=κ in E4 .
The purpose of this article is to investigate lacunary ideal convergence of sequences in neutrosophic normed space (NNS). Also, an original notion, named lacunary convergence of sequence in NNS, is defined. Also, lacunary $% \mathcal{I}$-limit points and lacunary $\mathcal{I}$-cluster points of sequences in NNS have been examined. Furthermore, lacu...
Based on the concept of lacunary statistical convergence of sequences of fuzzy numbers, the lacunary statistical convergence, uniformly lacunary statistical convergence, and equi-lacunary statistical convergence of double sequences of fuzzy-valued functions are defined and investigated in this paper. The relationship among lacunary statistical conv...
We investigate the concepts of pointwise and uniform I θ -convergence and type of convergence lying between mentioned convergence methods, that is, equi-ideally lacunary convergence of sequences of fuzzy valued functions and acquire several results. We give the lacunary ideal form of Egorov’s theorem for sequences of fuzzy valued measurable functio...
In this study, we define the concept of I statistically convergence for difference sequences and we use an Orlicz function to obtain more general results. We also show that an ΔI statistically convergent sequence with an Orlicz function is ΔI statistically pre-Cauchy.
We consider an astrohelicoidal hypersurface which its profile curve has astroid curve in the four dimensional Euclidean space E 4 . We also calculate Gaussian curvature and the mean curvature, and Weingarten relation of the hypersurface. Moreover, projecting hypersurface into 3-spaces, we draw some figures.
In this paper, we have investigated I 2 - λ -statistically convergence for double sequences in fuzzy normed linear spaces, where λ = (λ r) and μ = (μ s) be two non-decreasing sequences of positive real numbers, each tending to ∞ and such that λ r+1 ≤ λ r + 1, λ 1 = 1; μ s+1 ≤ μ s + 1, μ 1 = 1. Some inclusion relations between I 2 -statistically con...
We consider Ulisse Dini-type helicoidal hypersurfaces with timelike axis in Minkowski 4-space E 1 4 . Calculating the Gaussian and the mean curvatures of the hypersurfaces, we demonstrate some special symmetries for the curvatures when they are flat and minimal.
In this paper, we define four types of convergence of a sequence of random variables, namely, $\mathcal{I}$-statistical convergence of order $ \alpha $, $\mathcal{I}$-lacunary statistical convergence of order $\alpha $, strongly $\mathcal{I}$-lacunary convergence of order $\alpha $ and strongly $ \mathcal{I}$-Cesaro summability of order $\alpha $ i...
In this paper, we define m-uniform I -statistical convergence, (delta;m)-uniform I-lacunary statistical convergence and (Idelta;m)-uniform strongly p-lacunary summability on a arbitrary time scale. Also, by using m-uniform and (lamda;m)-uniform density of the subset of the time scale, we will focus on constructing concepts of (I lamda;m)-uniform st...
In this paper, we introduce and study the notion of rough \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal {I}_{2}$\end{document}I2-lacunary statistical converge...
