\(Δ\)-Convergence and Uniform Distribution in Lacunary Sense - Aris, B.; Küçükaslan, Mehmet (Communications in Mathematics and Applications, 2017)
In this paper, by considering usual partition of \([0, \infty)\) \(\Delta\)-convergence of non-negative real valued sequences is defined. It is shown that every convergent sequence is \(\Delta\)-convergence but the converse is not true, in general. Besides, some basic properties of \(\Delta\)-convergence as well as the second part of this paper by using any lacunary sequences as a partition of non-negative real numbers, lacunary uniform distribution is defined and some inclusion result between uniform distribution modulo 1 and lacunary uniform distribution has been given.
Keywords: Convergence of sequence; Statistically convergence; Uniformly distribution of sequence; Lacunary convergence