A generalization of natural density

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DOI:

https://doi.org/10.26637/mjm403/006

Abstract

The concept of natural density is generalized. It is proved that the new theory is consistent with the existing theory in the literature. Many new results were obtained. A theorem analogous to the Riemann’s theorem on rearrangement of non-absolutely convergent series is proved in the sense of generalized natural density. Some more possible generalizations are suggested.

Keywords:

Natural density

Mathematics Subject Classification:

35Q30
  • R. Vembu Department of Mathematics, SBK College, Aruppukottai - 626 101. India.
  • A. Bowrna Department of Mathematics, Sri Ramanas Arts and Science College for Women, Aruppukottai, India.
  • Pages: 388-391
  • Date Published: 01-07-2016
  • Vol. 4 No. 03 (2016): Malaya Journal of Matematik (MJM)

E. Artin and P. Seherk, On the Sum of Two Sets of Integers, Ann. of Math. 44 (1943), 138-142. DOI: https://doi.org/10.2307/1968760

P. Erdos and J. Suranyi, Topics in the Theory of Numbers, Springer (2003).

G. Grekos, Open problems on densities, in Number Theory and Applications, Proceedings of the International Conference on Number Theory and Cryptography (Allahabad, India, February 23-27, 2007), Hindustan Book Agency, New Delhi, 2009, 55-63. DOI: https://doi.org/10.1007/978-93-86279-46-0_6

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Published

01-07-2016

How to Cite

R. Vembu, and A. Bowrna. “A Generalization of Natural Density”. Malaya Journal of Matematik, vol. 4, no. 03, July 2016, pp. 388-91, doi:10.26637/mjm403/006.

Issue

Vol. 4 No. 03 (2016): Malaya Journal of Matematik (MJM)

Section

Articles

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Copyright (c) 2016 MJM

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This work is licensed under a Creative Commons Attribution 4.0 International License.

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