Statistical Convergence of Complex Uncertain Sequences

2017 ◽  
Vol 13 (03) ◽  
pp. 359-374 ◽  
Author(s):  
Binod Chandra Tripathy ◽  
Pankaj Kumar Nath
Keyword(s):  
Statistical Convergence ◽  
Complex Numbers ◽  
Convergence In Distribution ◽  
Convergence In Measure ◽  
Uncertain Variables ◽  
Model Complex ◽  
Uncertainty Space ◽  
Convergence Almost Surely ◽  
Decomposition Theorems ◽  
Convergence In Mean

Complex uncertain variables are measurable functions from an uncertainty space to the set of complex numbers and are used to model complex uncertain quantities. This paper introduces the statistical convergence concepts of complex uncertain sequences: statistical convergence almost surely (a.s.), statistical convergence in measure, statistical convergence in mean, statistical convergence in distribution and statistical convergence uniformly almost surely (u.a.s.) In addition, decomposition theorems and relationships among them are discussed.

Convergence of Complex Uncertain Double Sequences

2020 ◽  
Vol 16 (03) ◽  
pp. 447-459 ◽  
Author(s):  
Debasish Datta ◽  
Binod Chandra Tripathy
Keyword(s):  
Complex Numbers ◽  
Convergence In Distribution ◽  
Double Sequences ◽  
Convergence In Measure ◽  
Uncertain Variables ◽  
Mean Convergence ◽  
Model Complex ◽  
Uncertainty Space ◽  
Convergence Almost Surely ◽  
Convergence In Mean

Complex uncertain variables are measurable functions from an uncertainty space to the set of complex numbers and are used to model complex uncertain quantities. This paper introduces the convergence concepts of convergence almost surely (a.s.), convergence in measure, convergence in mean, convergence in distribution and convergence uniformly almost surely complex uncertain double sequences. In addition, relationships among the introduced classes of sequences have been introduced.

On rough convergence of complex uncertain sequences

2021 ◽  
Author(s):  
Shyamal Debnath ◽  
Bijoy Das
Keyword(s):  
Complex Numbers ◽  
Convergence In Distribution ◽  
Convergence In Measure ◽  
Uncertain Variables ◽  
Measurable Functions ◽  
Model Complex ◽  
Uncertainty Space ◽  
Convergence In Mean

Complex uncertain variables are measurable functions from an uncertainty space to the set of complex numbers and are used to model complex uncertain quantities. The main purpose of this paper is to introduce rough convergence of complex uncertain sequences and study some convergence concepts namely rough convergence in measure, rough convergence in mean, rough convergence in distribution of complex uncertain sequences. Lastly some relationship between them have been investigated.

scholarly journals On rough convergence variables of triple sequences

Analysis ◽  
2020 ◽  
Vol 40 (2) ◽  
pp. 85-88
Author(s):  
Nagarajan Subramanian ◽  
Ayhan Esi
Keyword(s):  
Convergence In Distribution ◽  
Fundamental Theory ◽  
Mathematical Properties ◽  
Convergence Almost Surely ◽  
The Relationship ◽  
Convergence In Mean

AbstractTriple sequence convergence plays an extremely important role in the fundamental theory of mathematics. This paper contains four types of convergence concepts, namely, convergence almost surely, convergence incredibility, trust convergence in mean, and convergence in distribution, and discuss the relationship among them and some mathematical properties of those new convergence.

scholarly journals On rough convergence variables of triple sequences

2018 ◽  
Vol 22 ◽  
pp. 01059
Author(s):  
M. Kemal Ozdemir ◽  
Ayhan Esi ◽  
Ayten Esi
Keyword(s):  
Basic Theory ◽  
Convergence In Distribution ◽  
Mathematical Properties ◽  
Important Position ◽  
Convergence Almost Surely ◽  
Convergence In Mean

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.

scholarly journals Lacunary Statistical Convergence in Measure for Double Sequences of Fuzzy Valued Functions

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Ömer Kişi
Keyword(s):  
Statistical Convergence ◽  
Double Sequence ◽  
Finite Measure ◽  
Measurable Space ◽  
Double Sequences ◽  
Convergence In Measure ◽  
Measurable Functions ◽  
Lacunary Statistical Convergence ◽  
Convergence Of Sequences ◽  
Sequences Of Fuzzy Numbers

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 convergence, uniformly lacunary statistical convergence, equi-lacunary statistical convergence of double sequences of fuzzy-valued functions, and their representations of sequences of α -level cuts are discussed. In addition, we obtain the lacunary statistical form of Egorov’s theorem for double sequences of fuzzy-valued measurable functions in a finite measurable space. Finally, the lacunary statistical convergence in measure for double sequences of fuzzy-valued measurable functions is examined, and it is proved that the inner and outer lacunary statistical convergence in measure are equivalent in a finite measure set for a double sequence of fuzzy-valued measurable functions.

scholarly journals Strongly almost convergent generalized difference sequences associated with multiplier sequences

2007 ◽  
Vol 57 (4) ◽  
Author(s):  
Ayhan Esi ◽  
Binod Tripathy
Keyword(s):  
Statistical Convergence ◽  
Sequence Spaces ◽  
Complex Numbers ◽  
Difference Sequence ◽  
Difference Sequences ◽  
Inclusion Relations ◽  
Difference Sequence Spaces ◽  
Convergent Sequences

AbstractLet Λ = (λk) be a sequence of non-zero complex numbers. In this paper we introduce the strongly almost convergent generalized difference sequence spaces associated with multiplier sequences i.e. w 0[A,Δm,Λ,p], w 1[A,Λm,Λ,p], w ∞[A,Δm,Λ,p] and study their different properties. We also introduce ΔΛm-statistically convergent sequences and give some inclusion relations between w 1[Δm,λ,p] convergence and ΔΛm-statistical convergence.

scholarly journals HUBUNGAN ANTARA KONVERGEN HAMPIR PASTI, KONVERGEN DALAM PELUANG, DAN KONVERGEN DALAM SEBARAN

2013 ◽  
Vol 2 (2) ◽  
pp. 10
Author(s):  
Vira Agusta ◽  
Dodi Devianto ◽  
Hazmira Yozza
Keyword(s):  
Probability Space ◽  
Random Variable ◽  
Convergence In Probability ◽  
Convergence In Distribution ◽  
Convergence Almost Surely ◽  
The Relationship

Let fXng be a sequence of random variable dened on a probability space ( ; F; P). In this paper, we studied about the relationship between the convergence almost surely, convergence in probability, and convergence in distribution. If the sequenceof random variable convergence almost surely to a random variable X then fXng convergence in probability to X. If the sequence of random variable fXng convergence in probability to a random variable X then fXng convergence in distribution to X.

scholarly journals Remarks on uniform convergence of random variables and statistics

2012 ◽  
Vol 45 (2) ◽  
Author(s):  
Wojciech Niemiro ◽  
Ryszard Zieliński
Keyword(s):  
Uniform Convergence ◽  
Random Variables ◽  
Convergence In Distribution ◽  
Convergence Almost Surely

AbstractConvergence in distribution, convergece in probability, and convergence almost surely,

Tauberian conditions under which statistical convergence follows from statistical summability by weighted means

2004 ◽  
Vol 41 (4) ◽  
pp. 391-403 ◽  
Author(s):  
Ferenc Móricz ◽  
Cihan Orhan
Keyword(s):  
Finite Number ◽  
Large Class ◽  
Statistical Convergence ◽  
Sufficient Conditions ◽  
Complex Numbers ◽  
Real Numbers ◽  
Tauberian Conditions ◽  
Summability Methods ◽  
Weighted Means ◽  
Necessary And Sufficient

The first named author has recently proved necessary and sufficient Tauberian conditions under which statistical convergence (introduced by H. Fast in 1951) follows from statistical summability (C, 1). The aim of the present paper is to generalize these results to a large class of summability methods (,p) by weighted means. Let p = (pk : k = 0,1, 2,...) be a sequence of nonnegative numbers such that po > 0 and Let (xk) be a sequence of real or complex numbers and set for n = 0,1, 2,.... We present necessary and sufficient conditions under which the existence of the limit st-lim xk = L follows from that of st-lim tn = L, where L is a finite number. If (xk) is a sequence of real numbers, then these are one-sided Tauberian conditions. If (xk) is a sequence of complex numbers, then these are two-sided Tauberian conditions.

Autocontinuity, convergence in measure, and convergence in distribution

1997 ◽  
Vol 92 (2) ◽  
pp. 197-203 ◽  
Author(s):  
Toshiaki Murofushi ◽  
Michio Sugeno ◽  
Manabu Suzaki
Keyword(s):  
Convergence In Distribution ◽  
Convergence In Measure
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