# Application of f-lacunary statistical convergence to approximation theorems

@article{Bhardwaj2018ApplicationOF,
title={Application of f-lacunary statistical convergence to approximation theorems},
author={Vinod Kumar Bhardwaj and Shweta Dhawan},
journal={Journal of Inequalities and Applications},
year={2018},
volume={2018}
}
• Published 11 October 2018
• Mathematics
• Journal of Inequalities and Applications
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). The main object of this paper is to prove Korovkin type approximation theorems using the notion of f-lacunary statistical convergence. A relationship between the newly established Korovkin type approximation theorems via f-lacunary statistical convergence, the classical Korovkin…
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## References

SHOWING 1-10 OF 39 REFERENCES
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
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
Korovkin type approximation theorems for weighted αβ-statistical convergence
• Mathematics
• 2015
The concept of αβ-statistical convergence was introduced and studied by Aktuuglu (Korovkin type approximation theorems proved via αβ-statistical conver- gence, J Comput Appl Math 259:174-181, 2014).
Korovkin and Weierstrass Approximation via Lacunary Statistical Sequences
• Mathematics
• 2005
In this study we shall extended Korovkin and Weierstrass approximation theorem to lacunary statistical convergent sequences. In addition, to these approximation theorems, we established also
Statistical lacunary summability and a Korovkin type approximation theorem
• Mathematics, Philosophy
• 2011
In this paper, we introduce statistical lacunary summability and strongly θq-convergence (0 < q < ∞) and establish some relations between lacunary statistical convergence, statistical lacunary
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
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.