Triple Sequence Research Articles

Generalized Rough Cesaro and Lacunary Statistical Triple Difference Sequence Spaces in Probability of Fractional Order Defined by Musielak-Orlicz Function

We generalized the concepts in probability of rough Ces$\grave{a}$ro and lacunary statistical by introducing the difference operator $\Delta^{\alpha}_{\gamma}$ of fractional order, where $\alpha$ is a proper fraction and $\gamma=\left(\gamma_{mnk}\right)$ is any fixed sequence of nonzero real or complex numbers. We study some properties of this operator involving lacunary sequence $\theta$ and arbitrary sequence $p=\left(p_{rst}\right)$ of strictly positive real numbers and investigate the topological structures of related with triple difference sequence spaces. The main focus of the present paper is to generalized rough Ces$\grave{a}$ro and lacunary statistical of triple difference sequence spaces and investigate their topological structures as well as some inclusion concerning the operator $\Delta^{\alpha}_{\gamma}.$

Bernstein operator of rough $I-$ core of triple sequences

Bernstein operator of rough $I-$ core of triple sequences

The Rough Intuitionistic Fuzzy Zweier Lacunary Ideal Convergence of Triple Sequence Spaces

We introduced and studied the concept of I-convergence of triple sequences in metric spaces where I is an ideal. The concept of I-convergence has a wide application in the field of number theory, trigonometric series, summability theory, probability theory, optimization and approximation theory. In this article, we introduce rough intuitionistic fuzzy Lacunary ideal convergent of triple sequence spaces via zwier operators. We discuss general topological properties.

On rough convergence variables of triple sequences

Triple sequence convergence has an extremly important position in the basic theory of mathematics. The present manuscript contains four types of convergence concept of convergence almost surely, convergence incredibility, trust convergence in mean and convergence in distribution and discuss the relation ship among those and some mathematical properties of those new convergence.

Bernstein operator of rough I-core of triple sequences

We introduce and study some basic properties of Bernstein-Stancu polynomials of rough I-convergent of triple sequence spaces and also study the set of all Bernstein-Stancu polynomials of rough I-limits of a triple sequence spaces and relation between analytic ness and Bernstein-Stancu polynomials of rough I-core of a triple sequence spaces.

On triple sequence of Bernstein operator of weighted rough I_λ-convergence

On triple sequence of Bernstein operator of weighted rough I_λ-convergence

Wijsman Rough Lacunary Statistical Convergence on I Cesaro Triple Sequences

In this paper, we defined concept of Wijsman I-Cesaro summability for sequences of sets and investigate the relationships between the concepts of Wijsman strongly I-Cesaro summability and Wijsman statistical I− Cesaro summability by using the concept of a triple sequence spaces.

Statistically pre-Cauchy triple sequences and Orlicz functions

Statistically pre-Cauchy triple sequences and Orlicz functions

On Triple sequence space of Bernstein operator of Rough I- convergence pre-cauchy sequences

We introduce and study some basic properties of rough I- convergentpre-Cauchy sequences of triple sequence of Bernstein polynomials and also study the set of all rough I- limits of a pre-Cauchy sequence of triple sequence of Bernstein polynomials and relation between analytic ness and rough I- statistical convergence of pre-Cauchy sequence of a triple sequences of Bernstein polynomials .

Rough statistical convergence on triple sequences

In this paper, using the concept of natural density, we introduce the notion of rough statistical convergence of triple sequences. We define the set of rough statistical limit points of a triple sequence and obtain rough statistical convergence criteria associated with this set. Later, we prove this set is closed and convex and also examine the relations between the set of rough statistical cluster points and the set of rough statistical limit points of a triple sequence.

Regular matrix transformation on triple sequence spaces

The main aim of this paper is to introduce the necessary and sufficient condition for a particular type of transformation of the form A: (a......) be regular from a triple sequence space to another triple sequence space.

Six dimensional matrix summability of triple sequences

In this paper we introduced the RH-regularity condition of six dimensional matrix. Matrix summability is one of the important tool used to characterize sequence spaces. In 2004 Patterson presented such a characterization of bounded double sequence using four dimensional matrix. Our main aim is to extend Patterson result in triple sequence spaces using six dimensional matrix transformations.

Wijsman Rough λ Statistical Convergence of Order α of Triple Sequence of Functions

In this paper, using the concept of natural density, we introduce the notion of Wijsman rough λ statistical convergence of order α triple sequence of functions. We define the set of Wijsman rough λ statistical convergence of order α of limit points of a triple sequence spaces of functions and obtain Wijsman λ statistical convergence of order α criteria associated with this set. Later, we prove that this set is closed and convex and also examine the relations between the set of Wijsman rough λ statistical convergence of order α of cluster points and the set of Wijsman rough λ statistical convergence of order α limit points of a triple sequences of functions.

The Ces$\grave{a}$ro convergence of triple sequence spaces of $\chi^{3}$ of fuzzy real numbers defined by a sequence of Musielak-Orlicz functions

We have to find the necessary and sufficient Tauberian conditions of convergence follows form $\left[C,1,1,1\right]-$ convergence of triple sequence spaces of $\chi^{3}$ of fuzzy numbers.

Some I-convergent triple sequence spaces defined by a sequence of modulus function

In this article we introduce the notion of I-convergent triple sequence spaces cOI3(F), cI3(F), l00I3(F), mI3(F) and mOI3(F) defined by a sequence of modulii F = (fpqr) and study some of their algebraic and topological properties like solidity, symmetricity, convergence free etc. We also prove some inclusion relation involving these sequence spaces.

Generalised triple difference of rough intuitionistic statistical convergence in probability of fractional order defined by Musielak-Orlicz function

We generalised the concepts in probability of rough intuitionistic convergence and rough intuitionistic statistically convergence by introducing the generalised difference operator Δαγ of fractional order, where α is a proper fraction and γ = (γmnk) is any fixed sequence of non-zero real or complex numbers. We study some properties of this operator and investigate the topological structures of related of triple difference sequence spaces of ξ 3f (Δαγ xmnk). The main focus of the present paper is to generalised rough intuitionistic convergence and rough intuitionistic statistical difference of triple difference sequence spaces of χ3 and investigate their topological structures as well as some interesting results concerning the operator Δαγ.

Riesz Triple Almost Lacunary χ3 Sequence Spaces Defined by a Orlicz Function-II

The aim of this paper is to introduce a new concept for strong almost Pringsheim convergence with respect to an Orlicz function, combining with Riesz mean for triple sequences and a triple lacunary sequence. We also introduce and study statistics convergence of Riesz almost lacunary χ3 sequence spaces and also some inclusion theorems are discussed.

Concurrent Exercise-Associated Ventricular Complexes and a Prolonged QT Interval are Associated with Evidence of Myocarditis

Background: Precise myocardial tissue characterization in subjects with exercise-associated ventricular ectopy and prolonged QT interval but no obvious structural heart disease might facilitate further risk stratification. There is no data assessing QT intervals in patients with exercise-associated premature ventricular complexes (PVCs). Cardiovascular magnetic resonance (CMR) enables us to non-invasively assess myocardial scar and oedema. The purpose of our study was to assess the QT intervals in patients with exercise-associated premature ventricular complexes (PVCs). Methods: We analyzed the QT and QTc intervals of the 162 consecutive patients with documented exerciseassociated PVCs but no history or evidence of coronary heart disease or cardiomyopathy we previously examined. Findings were compared with those from 182 new controls without exercise-associated PVCs matched for gender and age. Continuous 12-holder ECG during upright bicycle exercise test and ECG-triggered, T2-weighted, fast spin echo triple inversion recovery sequences and late gadolinium enhancement were obtained, as were LV function and dimensions. Results: QT and QTc intervals were significantly prolonged in patients compared to controls (396.3 ± 33.5 ms vs. 385.9 ± 28.4 ms, p=0.002 and 431.7 ± 26.2 ms vs. 419.9 ± 26.6 ms, p=0.0001). Eighty five percent of patients with exercise-associated PVCs and prolonged QT intervals had structural abnormalities in the myocardium suggestive of acute or remote myocarditis or myopericarditis. Conclusion: Patients with exercise-associated PVCs showed prolonged QT intervals compared to controls. As a long QT interval is predictive of increased risk for arrhythmias or sudden cardiac death these findings may supply a potential mechanism for explaining the increased risk of some patients with exercise-associated PVCs.

Statistical Extensions of Some Classical Tauberian Theorems for Cesàro Summability of Triple Sequences

In (Canak and Totur, Georgian Math J 23(1):33–42, 2016), Canak and Totur have extended some classical Tauberian theorems for single sequences to triple sequences. In (Fridy and Khan, Proc Am Math Soc 128:2347–2355, 2000), Fridy and Khan obtained statistical extensions of some classical Tauberian theorems. The concept of statistical convergence for triple sequences has been introduced by Şahiner et al. (Selcuk J Appl Math 8(2):49–55, 2007). In this paper, we investigate Tauberian conditions for the statistical convergence and statistical (C,1,1,1) summability of triple sequences.

Dual and triple equations and q-orthogonal polynomials

In this paper, we solve dual and triple sequences involving q-orthogonal polynomials. We also introduce and solve a system of dual series equations when the kernel is the q-Laguerre polynomials. Examples are included.