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Filomat
In this paper we have extended the concepts of I-limit superior and I-limit inferior to I-statistical limit superior and I-statistical limit inferior and studied some of their properties for sequence of real numbers.
Proyecciones (Antofagasta), 2021
In this paper we investigate the notion of I-statistical ϕ-convergence and introduce IS-ϕ limit points and IS-ϕ cluster points of real number sequence and also studied some of its basic properties.
Azerbaijan Journal of Mathematics Print Issn 2218 6816 Online Issn 2221 9501, 2014
In this paper, the concept of A-statistical supremum (sup A x) and A-statistical infumum (inf A x) for real valued sequences x = (x n ) are defined and studied. It is mainly shown that, the equality of supA x and inf A x is necessary but not sufficient for to existence of usual limit of the sequence. On the other hand, the equality of sup A x and inf A x is necessary and sufficient for to existence of A-statistical limit of the real valued sequences.
Fuzzy Sets and Systems, 2006
In this paper, we extend the concepts of statistical limit superior and limit inferior (as introduced by Fridy and Orhan [Statistical limit superior and limit inferior, Proc. Amer. Math. Soc. 125 (12) (1997) 3625-3631. [12]]) to statistically bounded sequences of fuzzy numbers and give some fuzzy-analogues of properties of statistical limit superior and limit inferior for sequences of real numbers.
2013
The main aim of this paper is to investigate properties of statistically convergent sequences. Also, the denition of statistical mono- tonicity and upper (or lower) peak points of real valued sequences will be introduced. The interplay between the statistical convergence and these concepts are also studied. Finally, the statistically monotonicity is gener- alized by using a matrix transformation.
Proyecciones (Antofagasta), 2019
In this paper we have extended the notion of λ-statistical limit points of real sequences to I λ-statistical limit points and studied some basic properties of the set of all I λ-statistical limit points and I λ-statistical cluster points of real sequences including their interrelationship. Then we have established I λ-statistical analogue of the monotone sequence theorem. Also introducing additive property of I λ-density zero sets we have established its relationship with I λ-statistical convergence. Keywords I λ-statistical convergence, I λ-statistical limit point, I λ-statistical cluster point, I λ-density, I λ-statistical boundedness.
Malaya Journal of Matematik, 2021
In this paper we have extended the notion of λ -statistical limit points of real sequences to I λ -statistical limit points and studied some basic properties of the set of all I λ -statistical limit points and I λ -statistical cluster points of real sequences including their interrelationship. Then we have established I λ -statistical analogue of the monotone sequence theorem. Also introducing additive property of I λ -density zero sets we have established its relationship with I λ -statistical convergence. I λ -statistical convergence, I λ -statistical limit point, I λ -statistical cluster point, I λ -density, I λ -statistical boundedness.
Journal of the Indonesian Mathematical Society
By using modulus functions, we have obtained a generalization of statistical convergence of asymptotically equivalent sequences, a new non-matrix convergence method, which is intermediate between the ordinary convergence and the statistical convergence. Further, we have examined some inclusion relations related to this concept.
Tamkang Journal of Mathematics, 2012
For an admissible ideal I ⊆ P (N) and a non-decreasing real sequence λ = (λ n) tending to ∞ with λ n+1 ≤ λ n +1, λ 1 = 1, the objective of this paper is to introduce the new notions I −statistically equivalent, I − [V, λ]−equivalent and I − λ−statistically equivalent. which are natural combinations of the definitions for asymptotically equivalent, statistical limit, λ−statistical limit and I −limit for number sequences. In addition, some relations among these new notions are also obtained.
2004
In the paper [5] the concept of I-convergence is introduced. This concept is a generalization of the statistical convergence. In this paper some notions and results from the statistical convergence are extended to the Iconvergence.
Miskolc Mathematical Notes, 2017
In this paper we define generalized statistical convergence for sequences of sets of order˛; 0 <˛Ä 1 in sense of Wijsman and study some basic properties of this concept.
Applied Mathematics E Notes, 2013
The aim of the present paper is to give some properties of A-statistical convergence of sequences. We give de…nition of A-statistical monotonicity, upper and lower peak points of sequences. The relation between these concepts and A-statistical monotonicity is investigated. Also, some results given in [11] are generalized.
Journal of Mathematical Analysis and Applications, 1996
Ž . This article extends the concept of a statistical limit cluster point of a sequence Ž .
Mathematical Communications, 2006
We investigate the connectedness and Baire classification of a function associated with the statistical limit superior.
Applied Mathematics and Computation, 2009
We investigate the structure of the set of all statistical limit points of a double sequence and prove certain results, mainly showing that this set can be characterized as a F r -set.
Journal of Inequalities and Applications, 2013
In this paper we study the notion of statistical ( A , λ ) -summability, which is a generalization of statistical A-summability. We study here many other related concepts and its relations with statistical convergence and λ-statistical convergence and provide some interesting examples.
arXiv: Functional Analysis, 2016
The concept of I-statistical convergence of sequence was first defined by Das et.al [2]. In this paper we introduce and study the notion of rough I-statistical convergence of sequence in normed linear Spaces. We also define the set of rough I-statistical limits of a sequence and discuss some topological properties of this set.
Filomat, 2014
In this paper we study the concepts of Wijsman I-statistical convergence, Wijsman I-lacunary statistical convergence and Wijsman strongly I-lacunary convergence of sequences of sets and investigate the relationship between them.
Acta Mathematica Hungarica, 2007
We introduce the concept of the statistical limit (at ∞) of a measurable function in several variables and recall the concept of the statistical convergence of a multiple sequence. Then we extend a classical theorem of Schoenberg (which characterizes statistical convergence) from single to multiple sequences, and prove an analogous theorem on statistical limit. These theorems even may be extended to vector-valued sequences or functions, respectively.
2008
This paper presents new definitions which are a natural combination of the definition for asymptotically equivalence ∆−lacunary statistically convergence. Using this definitions we have proved the Sθ (∆)-asymptotically equivalence analogues theorems of [5] and [6].
Symmetry
In this paper, we defined weighted (Eλ,q)(Cλ,1) statistical convergence. We also proved some properties of this type of statistical convergence by applying (Eλ,q)(Cλ,1) summability method. Moreover, we used (Eλ,q)(Cλ,1) summability theorem to prove Korovkin’s type approximation theorem for functions on general and symmetric intervals. We also investigated some of the results of the rate of weighted (Eλ,q)(Cλ,1) statistical convergence and studied some sequences spaces defined by Orlicz functions.
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