Density by Moduli and Statistical Boundedness

@article{Bhardwaj2016DensityBM,
  title={Density by Moduli and Statistical Boundedness},
  author={Vinod Kumar Bhardwaj and Shweta Dhawan and Sandeep Gupta},
  journal={Abstract and Applied Analysis},
  year={2016},
  volume={2016},
  pages={1-6}
}
We have generalized the notion of statistical boundedness by introducing the concept of -statistical boundedness for scalar sequences where is an unbounded modulus. It is shown that bounded sequences are precisely those sequences which are -statistically bounded for every unbounded modulus . A decomposition theorem for -statistical convergence for vector valued sequences and a structure theorem for -statistical boundedness have also been established. 
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12 Citations
Background Citations
2
Methods Citations
4

12 Citations

Density by Moduli and Lacunary Statistical Convergence
We have introduced and studied a new concept of -lacunary statistical convergence, where is an unbounded modulus. It is shown that, under certain conditions on a modulus , the concepts of lacunary…
On Asymptotically f-Statistical Equivalent Sequences
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…
Asymptotically deferred f-statistical equivalence of sequences
In this work, we obtain a generalization of asymptotically deferred statistical equivalence of non-negative real-valued sequences with the aid of a modulus function. Further, we examine some of main…
Density by moduli and Wijsman statistical convergence
In this paper, we generalized the Wijsman statistical convergence of closed sets in metric space by introducing the $f$-Wijsman statistical convergence these of sets, where $f$ is an unbounded…
On deferred statistical boundedness of order α
In this paper, we introduce and examine the concept of deferred statistical boundedness of order α and give the relation between statistical boundedness and deferred statistical boundedness of orde...
Some Relations Between the Sets of f-Statistically Convergent Sequences
In this study we first established the relations between f-density and g-density of a subset of the set of positive integers for any modulus functions f and g. Using the obtained facts we establish…
Density by moduli and Wijsman lacunary statistical convergence of sequences of sets
TLDR
It is shown that, under certain conditions on a modulus f, the concepts of Wijsman lacunary strong convergence with respect to amodulus f and f-Wijs man lacunARY statistical convergence are equivalent on bounded sequences.
On Asymptotically f-statistical Equivalent Set Sequences in the Sense of Wijsman
The aim of this paper is to introduce a generalization of statistical convergence of asymptotically equivalent set sequences and examine some inclusion relations related to a new concept of Wijsman…
KOROVKIN TYPE APPROXIMATION THEOREMS VIA f-STATISTICAL CONVERGENCE
The concept of f -statistical convergence which is, in fact, a generalization of statistical convergence, and is intermediate between the ordinary convergence and the statistical convergence, has…
f-Statistical convergence of order α and strong Cesàro summability of order α with respect to a modulus
In this paper, following a very recent and new approach of Aizpuru et al. (Quaest. Math. 37:525-530, 2014), we further generalize a concept of α-density to that of fα$f_{\alpha}$-density, where f is…
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References

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