(\Delta\)-Convergence and Uniform Distribution in Lacunary Sense
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 \(\Delta\)-conver...
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Veröffentlicht in: | Communications in Mathematics and Applications 2017-01, Vol.8 (1), p.69 |
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Hauptverfasser: | , |
Format: | Artikel |
Sprache: | eng |
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Zusammenfassung: | 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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ISSN: | 0976-5905 0975-8607 |
DOI: | 10.26713/cma.v8i1.578 |