# 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}
}
• Published 10 February 2016
• Mathematics
• Abstract and Applied Analysis
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
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
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• 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
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
• Mathematics
Journal 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
• Mathematics
Communications 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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