\(\Delta\)-Convergence and Uniform Distribution in Lacunary Sense

Authors

  • B. Aris Department of Mathematic, Mersin University, Mersin
  • Mehmet Küçükaslan Department of Mathematic, Mersin University, Mersin

DOI:

https://doi.org/10.26713/cma.v8i1.578

Keywords:

Convergence of sequence, Statistically convergence, Uniformly distribution of sequence, Lacunary convergence

Abstract

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.

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Published

30-06-2017
CITATION

How to Cite

Aris, B., & Küçükaslan, M. (2017). \(\Delta\)-Convergence and Uniform Distribution in Lacunary Sense. Communications in Mathematics and Applications, 8(1), 69–86. https://doi.org/10.26713/cma.v8i1.578

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Section

Research Article