# 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.

## 12 Citations

Density by Moduli and Lacunary Statistical Convergence

- Mathematics
- 2016

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

- Mathematics
- 2018

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

- Mathematics
- 2018

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

- Mathematics
- 2016

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

- Mathematics
- 2021

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

- Mathematics
- 2019

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

- MathematicsJournal of inequalities and applications
- 2017

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

- MathematicsCommunications in Mathematics and Applications
- 2019

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

- Mathematics
- 2018

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

- Mathematics, Philosophy
- 2015

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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