2017
DOI: 10.1186/s13660-017-1512-y
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f ( λ , μ ) $f_{(\lambda,\mu)}$ -statistical convergence of order α̃ for double sequences

Abstract: New concepts of -statistical convergence for double sequences of order α̃ and strong -Cesàro summability for double sequences of order α̃ are introduced for sequences of (complex or real) numbers. Furthermore, we give the relationship between the spaces , and . Then we express the properties of strong -Cesàro summability of order β̃ which is related to strong -Cesàro summability of order α̃. Also, some relations between -statistical convergence of order α̃ and strong -Cesàro summability of order α̃ are given.

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Cited by 26 publications
(4 citation statements)
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“…Let be a topological space and be a sequence in . Then is said to be statistically convergent to whenever, for each neighborhood of , we have [13][14][15][16][17][18]. Similarly, a sequence in a locally solid Riesz space is said to be statisticallyconvergent to if it is provided that, for every -neighborhood of zero, holds.…”
Section: Introductionmentioning
confidence: 99%
“…Let be a topological space and be a sequence in . Then is said to be statistically convergent to whenever, for each neighborhood of , we have [13][14][15][16][17][18]. Similarly, a sequence in a locally solid Riesz space is said to be statisticallyconvergent to if it is provided that, for every -neighborhood of zero, holds.…”
Section: Introductionmentioning
confidence: 99%
“…Another generalization of the statistical convergence is known as weighted statistical convergence which was established by Karakaya and Chishti [20] in 2009 and gradually improved by Aizpuru et al [2], Cinar and Et [6,12], Das et al [9], Ghosal [16][17][18], Işik and Altin [19], Mursaleen et al [22] and Som [25].…”
Section: Introductionmentioning
confidence: 99%
“…1: If n = n; then (V; ) summability is reduced to Cesàro summability. By we denote the class of all non-decreasing sequence of positive real numbers tending to 1 such that n+1 n + 1; 1 = 1: = ( n ) sequence spaces were studied in ( [11], [12], [21], [27], [28], [13], [14], [29], [36]) and A statistical convergence for A = (a ik ) an in…nite matrix of complex numbers were studied in ( [15], [14], [37], [3], [4]).…”
Section: Introductionmentioning
confidence: 99%