Uniformly maldistributed sequences in a strict sense

Diophantine approximation generalized

“…The next theorem follows immediately from a criterion of continuity of d.f.s in [11,Theorem 2.3]. In [23] a uniformly maldistributed sequence (x n ) ∞ n=1 is characterized by the fact that the set G((x n ) ∞ n=1 ) contains all one-step d.f.s c α (x). In the way of Theorem 1 for such (x n ) ∞ n=1 one can prove the following: Theorem 4.…”

“…Theorem 5 can also be applied in the following [23,Par. 12,Theorem]: By Theorem 5 there exists a sequence (z n ) ∞ n=1 , z n > 0, z n → 0, such that for n k , |x − x n k | < z n k ,…”

Statistical convergence of subsequences of a given sequence

“…In [24] a test for statistical convergence of bounded sequences is established which can be formulated in our terminology as follows:…”

Measure theory of statistical convergence

“…The notion of A-statistical convergence was first introduced by Connor in [5] in 1989, which has been investigated and developed by many mathematicians such as Connor in [2][3][4][5][6][7][8][9][10], Miller in [19,20], Kolk in [60][61][62][63], Fridy, Khan in [12,13], Demirici in [34][35][36][37], Savas in [99][100][101][102][103][104][105][106][107], Zeager in [121,122], Bilgin in [22][23][24][25][26], Duman, Khan, Orhan in [43][44][45][46][47]. Now, it has become a very common and useful notion.…”