### WEIGHTED STATISTICAL CONVERGENCE OF REAL VALUED SEQUENCES

DOI Number
https://doi.org/10.22190/FUMI2003887A
First page
887
Last page
898

#### Abstract

Functions defined in the form $g:\mathbb{N}\to[0,\infty)$ such that $\lim_{n\to\infty}g(n)=\infty$ and $\lim_{n\to\infty}\frac{n}{g(n)}=0$'' are called weight functions. Using the weight function, the concept of weighted density, which is a generalization of natural density, was defined by Balcerzak, Das, Filipczak and Swaczyna in the paper Generalized kinsd of density and the associated ideals'', Acta Mathematica Hungarica 147(1) (2015), 97-115.

In this study, the definitions of $g$-statistical convergence and $g$-statistical
Cauchy sequence for any weight function $g$ are given and it is proved that these two concepts are equivalent. Also some inclusions of the sets of all weight $g_1$-statistical convergent and weight $g_2$-statistical convergent sequences for $g_1,g_2$ which have the initial conditions are given.

#### Keywords

weight functions; natural density; statistical convergent sequences.

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#### References

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DOI: https://doi.org/10.22190/FUMI2003887A

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