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On $A$-statistical convergence and $A$-statistical Cauchy via ideal
Karpatsʹkì Matematičnì Publìkacìï, 2022 In [Analysis 1985, 5 (4), 301-313], J.A. Fridy proved an equivalence relation between statistical convergence and statistical Cauchy sequence. In this paper, we define $A^{I^{\ast }}$-statistical convergence and find under certain conditions, that it is ...
O.H. Edely, M. Mursaleen
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Application of f-lacunary statistical convergence to approximation theorems [PDF]
Journal of Inequalities and Applications, 2018 The concept of f-lacunary statistical convergence which is, in fact, a generalization of lacunary statistical convergence, has been introduced recently by Bhardwaj and Dhawan (Abstr. Appl. Anal. 2016:9365037, 2016).
Vinod K Bhardwaj, Shweta Dhawan
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Weighted A-Statistical Convergence for Sequences of Positive Linear Operators [PDF]
The Scientific World Journal, 2014 We introduce the notion of weighted A-statistical convergence of a sequence, where A represents the nonnegative regular matrix. We also prove the Korovkin approximation theorem by using the notion of weighted A-statistical convergence. Further, we give a
S. A. Mohiuddine +2 more
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Statistical Order Convergence and Statistically Relatively Uniform Convergence in Riesz Spaces [PDF]
Journal of Function Spaces, 2018 A new concept of statistically e-uniform Cauchy sequences is introduced to study statistical order convergence, statistically relatively uniform convergence, and norm statistical convergence in Riesz spaces.
Xuemei Xue, Jian Tao
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STATISTICAL CONVERGENCE IN A BICOMPLEX VALUED METRIC SPACE
Ural Mathematical Journal, 2023 In this paper, we study some basic properties of bicomplex numbers. We introduce two different types of partial order relations on bicomplex numbers, discuss bicomplex valued metric spaces with respect to two different partial orders, and compare them ...
Subhajit Bera, Binod Chandra Tripathy
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On Deferred Statistical Convergence of Sequences in Neutrosophic Normed Spaces [PDF]
Sahand Communications in Mathematical Analysis, 2022 In this paper, we introduce the notion of deferred statistical convergence in the neutrosophic normed spaces as an extension of statistical convergence, $\lambda$-statistical convergence, and lacunary statistical convergence.
Shyamal Debnath +2 more
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Theorems of Second Korovkin Type with respect to Triangular $A$-Statistical Convergence
Universal Journal of Mathematics and Applications, 2023 This article is a continuation of our previous works. We mainly investigate a Korovkin type theorem for double sequences of positive linear operators defined in the space of all $2\pi $-periodic and real valued continuous functions on the real two ...
Selin Çınar
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On Weak Statistical Convergence [PDF]
International Journal of Mathematics and Mathematical Sciences, 2007 The main object of this paper is to introduce a new concept of weak statistically Cauchy sequence in a normed space. It is shown that in a reflexive space, weak statistically Cauchy sequences are the same as weakly statistically convergent sequences. Finally, weak statistical convergence has been discussed inlpspaces.
Vinod K. Bhardwaj, Indu Bala
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ON DISCRETE WEIGHTED STATISTICAL CONVERGENCE [PDF]
Facta Universitatis, Series: Mathematics and Informatics, 2021 In the present paper, the notion of discrete weighted mean method of summability isextended the concept of statistical convergence. We also give the notion of statistical (M,P_{λ})-summability and [M,P_{λ}]_{q}-summability.
Ercan, Sinan +2 more
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Lacunary statistical convergence [PDF]
Pacific Journal of Mathematics, 1993 The sequence \(x\) is statistically convergent to \(L\) provided that for each \(\varepsilon>0\), \[ \lim_ n {1 \over n} \{\text{the number of } k \leq n:| x_ k-L | \geq \varepsilon\}=0. \] A related concept is introduced by replacing the set \(\{k:k \leq n\}\) with \(\{ k:k_{r-1}
Fridy, J. A., Orhan, C.
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