Have a personal or library account? Click to login
On Commutation Properties of the Composition Relation of Convergent and Divergent Permutations (Part I) Cover

On Commutation Properties of the Composition Relation of Convergent and Divergent Permutations (Part I)

Open Access
|Aug 2014

References

  1. [1] AGNEW, R. P.: Permutations preserving convergence of series, Proc. Amer. Math. Soc. 6 (1955), 563-564.10.1090/S0002-9939-1955-0071559-4
  2. [2] BOREL, E.: Sur le changement de l’ordre des termes d’une série semi-convergente, Bull. Sci. Math. 14 (1890), 97-102.
  3. [3] BOURBAKI, N.: Topologie Générale. Hermann, Paris, 1951.
  4. [4] ČERVE NANSKY, J.-šALÀT, T.: Convergence preserving permutations on N and Fréchet’s space of permutations of N, Math. Slovaca 49 (1999), 189-199.
  5. [5] KRANTZ, S. G.-MCNEAL, J. D.: Creating more convergent series, Amer. Math. Monthly 111 (2004), 32-38.10.1080/00029890.2004.11920044
  6. [6] KRONROD, A. S.: On permutation of terms of numerical series, Mat. Sb. 18(60) (1946), 237-280. (In Russian)
  7. [7] LEVI, F. W.: Rearrangements of convergent series, Duke Math. J. 13 (1946), 579-585.10.1215/S0012-7094-46-01348-8
  8. [8] NASH-WILIAMS, C. ST. J. A.-WHITE, D. J.: An application of network flows to rearrangement of series, J. London Math. Soc. (2) 59 (1999), 637-646.10.1112/S0024610799007292
  9. [9] PLEASANTS, P. A. B.: Rearrangements that preserve convergence, J. Lond. Math. Soc. (2) 15 (1977), 134-142.10.1112/jlms/s2-15.1.134
  10. [10] PLEASANTS, P. A. B.: Addendum: Rearrangements that preserve convergence, J. Lond. Math. Soc. (2) 18 (1978), 576.10.1112/jlms/s2-18.3.576-s
  11. [11] SCHAEFER, P.: Sums of the rearranged series, College Math. J. 17 (1986), 66-70.10.1080/07468342.1986.11972931
  12. [12] STOUT, Q.: On Levi’s duality between permutations and convergent series, J. London Math. Soc. (2) 34 (1986), 67-80.10.1112/jlms/s2-34.1.67
  13. [13] WITUŁA, R.: Convergence-preserving functions, Nieuw Arch. Wiskd. (4) 13 (1995), 31-35.
  14. [14] WITUŁA, R.-SŁOTA, D.-SEWERYN, R.: On Erd¨os’ theorem for monotonic subsequences, Demonstratio Math. 40 (2007), 239-259.
  15. [15] WITUŁA, R.: On the set of limit points of the partial sums of series rearranged by a given divergent permutation, J. Math. Anal. Appl. 362 (2010), 542-552.10.1016/j.jmaa.2009.09.028
  16. [16] WITUŁA, R.: Algebraic and set-theoretical properties of some subsets of families of convergent and divergent permutations, Tatra Mt. Math. Publ. 55 (2013), 27-36.
  17. [17] WITUŁA, R.: The family F of permutations of N, Math. Slovaca (in print).
  18. [18] WITUŁA, R.: Decompositions of permutations of N with respect to the divergent permutations, in: Traditional and present-day topics in real analysis, Dedicated to Prof. J. S. Lipi´nski (M. Filipczak, E. Wagner-Bojakowska, eds.), Faculty of Math. and Comput. Sci., University of Łódz, Łódz University Press, Łódz, 2013, pp. 473-490.10.18778/7525-971-1.27
  19. [19] WITUŁA, R.: Algebraic properties of the convergent and divergent permutations, Filomat (to appear).
  20. [20] WITUŁA, R.: Some remarks about the group G generated by the family of convergent permutations (to appear).
  21. [21] WITUŁA, R.-HETMANIOK, E.-SŁOTA, D.: On commutation properties of the composition relation of permutations from family D(1). PART II (to appear).
DOI: https://doi.org/10.2478/tmmp-2014-0002 | Journal eISSN: 1338-9750 | Journal ISSN: 12103195
Language: English
Page range: 13 - 22
Submitted on: Feb 7, 2013
Published on: Aug 15, 2014
Published by: Slovak Academy of Sciences, Mathematical Institute
In partnership with: Paradigm Publishing Services
Publication frequency: 3 issues per year

© 2014 Roman Wituła, Edyta Hetmaniok, Damian Słota, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.