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 $g$-statisticalCauchy 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.
In this paper, for any arbitrary two primes p and q the relationship between the corresponding arithmetic functions (ap(n)) and (aq(n)) are investigated. Furthermore, a general formula for statistical density of all sets on which the two arithmetic function have the same value is also established.
In this paper, by using natural density of subsets of N, the statistical limit and cluster points of the arithmetical functions (ap (n)), γ (n),τ(n), Δ γ (n) and Δ τ (n) are studied. In addition to this, we also investigate statistical limit and cluster points of (Δ r γ (n) and (Δ r τ (n)) for each r ın N.
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