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Values of limit periodic sequences and functions

  • Michal Veselý EMAIL logo und Petr Hasil
Veröffentlicht/Copyright: 2. Mai 2016
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Mathematica Slovaca
Aus der Zeitschrift Mathematica Slovaca Band 66 Heft 1

Abstract

We consider limit periodic sequences and functions with values in pseudometric spaces. We construct limit periodic sequences and functions with given values. For any totally bounded countable set, we find a limit periodic sequence which attains each value from this set periodically. A corresponding result concerning such a construction of limit periodic functions is proved as well. For any totally bounded countable set which is dense in itself, we construct a limit periodic bijective map from the integers into this set. As corollaries, we obtain new results about non-almost periodic solutions of almost periodic transformable difference systems.

Keywords: limit periodic sequences; limit periodic functions; almost periodicity; asymptotic almost periodicity
MSC: Primary 11K31; 11K70; Secondary 39A06; 39A24; 42A75; 43A60; 46S40

The first author is supported by the project “Employment of Best Young Scientists for International Cooperation Empowerment” (CZ.1.07/2.3.00/30.0037) co-financed from European Social Fund and the state budget of the Czech Republic.

The second author is supported by the Czech Science Foundation under Grant P201/10/1032.

  1. This paper has been communicated by Gregor Dolinar

References

[1] Bânzaru T.: Multivalued almost periodic mappings, Bul. Științ. Tehn. Inst. Univ. Politeh. Timiș. Ser. Mat. Fiz. Mec. Teoret. Apl. 19(33) (1974), 25–28.Suche in Google Scholar

[2] Bânzaru T.—Crivăț N.: On almost periodic multivalued maps with values in uniform spaces, Bul. Științ. Tehn. Inst. Univ. Politeh. “Traian Vuia” Timiș. Ser. Mat. Fiz. 26(40) (1981), 47–51.Suche in Google Scholar

[3] Bede B.—Gal S. G.: Almost periodic fuzzy-number-valued functions, Fuzzy Sets and Systems 147 (2004), 385–403.10.1016/j.fss.2003.08.004Suche in Google Scholar

[4] Besicovitch A. S.: Almost Periodic Functions, Dover Publications, New York, 1955.Suche in Google Scholar

[5] Bochner S.: Abstrakte fastperiodische Funktionen, Acta Math. 61 (1933), 149–184.10.1007/BF02547790Suche in Google Scholar

[6] Bohr H.: Zur Theorie der fastperiodischen Funktionen. I. Eine Verallgemeinerung der Theorie der Fourierreihen, Acta Math. 45 (1925), 29–127.10.1007/BF02395468Suche in Google Scholar

[7] Bohr H.: Zur Theorie der fastperiodischen Funktionen. II. Zusammenhang der fastperiodischen Funktionen mit Funktionen von unendlich vielen Variabeln; gleichmässige Approximation durch trigonometrische Summen, Acta Math. 46 (1925), 101–214.10.1007/BF02543859Suche in Google Scholar

[8] Bugajewski D.—N’Guérékata G. M.: Almost periodicity in Fréchet spaces, J. Math. Anal. Appl. 299 (2004), 534–549.10.1016/j.jmaa.2004.05.042Suche in Google Scholar

[9] Cheban D. N.: Asymptotically Almost Periodic Solutions of Differential Equations, Hindawi Publishing Corporation, New York, 2009.10.1155/9789774540998Suche in Google Scholar

[10] Corduneanu C.: Almost Periodic Functions, John Wiley and Sons, New York, 1968.Suche in Google Scholar

[11] Corduneanu C.: Almost Periodic Oscillations and Waves, Springer, New York, 2009.10.1007/978-0-387-09819-7Suche in Google Scholar

[12] Crivăț N.: Almost periodic multifunctions with values in generalized uniform spaces, Bul. Științ. Univ. Politeh. Timiș. Ser. Mat. Fiz. 52(66) (2007), 69–75.Suche in Google Scholar

[13] Crivăț N.: Almost periodic multifunctions with values in generalized uniform spaces (II), Bul. Științ. Univ. Politeh. Timiș. Ser. Mat. Fiz. 55(69) (2010), 16–21.Suche in Google Scholar

[14] Duy T. K.: Limit-periodic arithmetical functions and the ring of finite integral adeles, Lith. Math. J. 51 (2011), 486–506.10.1007/s10986-011-9143-3Suche in Google Scholar

[15] Dvurečenskij A.: Pseudo MV-algebras are intervals in ℓ-groups, J. Aust. Math. Soc. 72 (2002), 427–445.10.1017/S1446788700036806Suche in Google Scholar

[16] Fan K.: Les fonctions asymptotiquement presque-périodiques d’une variable entière et leur application à l’étude de l’itération des transformations continues, Math. Z. 48 (1942/43), 685–711.10.1007/BF01180036Suche in Google Scholar

[17] Fink A. M.: Almost Periodic Differential Equations . Lecture Notes in Math. 377, Springer, Berlin, 1974.10.1007/BFb0070324Suche in Google Scholar

[18] Flor P.: Über die Wertmengen fastperiodischer Folgen, Monatsh. Math. 67 (1963), 12–17.10.1007/BF01300676Suche in Google Scholar

[19] Fréchet M.: Les fonctions asymptotiquement presque-périodiques, Revue Sci (Rev. Rose Illus.) 79 (1941), 341–354.Suche in Google Scholar

[20] Fréchet M.: Les fonctions asymptotiquement presque-périodiques continues, C. R. Acad. Sci. Paris 213 (1941), 520–522.Suche in Google Scholar

[21] Gal C. G.—GalS. G.—N’GuérékataG. M.: Almost automorphic functions with values in p -Fréchet spaces, Electron. J. Differential Equations 2008 (2008), No. 21, 1–18.Suche in Google Scholar

[22] Gal S. G.—N’GuérékataG. M.: Almost periodic functions with values in p -Fréchet spaces, 0 < p < 1, Glob. J. Pure Appl. Math. 3 (2007), 89–103.Suche in Google Scholar

[23] Hasil P.—Veselý M.: Almost periodic transformable difference systems, Appl. Math. Comput. 218 (2012), 5562–5579.10.1016/j.amc.2011.11.050Suche in Google Scholar

[24] Jajte R.: On almost-periodic sequences, Colloq. Math. 13 (1964/1965), 265–267.10.4064/cm-13-2-265-267Suche in Google Scholar

[25] Kelley J. L.: General Topology . Grad. Texts in Math. 27, Springer, New York, 1975.Suche in Google Scholar

[26] Latif M. A.—BhattiM. I.: Almost periodic functions defined on ℝn with values in fuzzy setting, Punjab Univ. J. Math. (Lahore) 39 (2007), 19–27.Suche in Google Scholar

[27] Latif M. A.—N’GuérékataG. M.—BhattiM. I.: Almost periodic functions defined on ℝn with values in p -Fréchet spaces, 0 < p < 1, Libertas Math. 29 (2009), 83–100.Suche in Google Scholar

[28] Levitan B. M.—ZhikovV. V.: Almost Periodic Functions and Differential Equations, Cambridge University Press, Cambridge, 1982.Suche in Google Scholar

[29] Mauclaire J.-L.: Suites limite-périodiques et théorie des nombres. I, Proc. Japan Acad. Ser. A Math. Sci. 56 (1980), 180–182.10.3792/pjaa.56.180Suche in Google Scholar

[30] Muni G.: Functions of 𝔖 almost periodic with respect to a homeomorphic group, Boll. Unione Mat. Ital. B (5) 17 (1980), 232–243.Suche in Google Scholar

[31] N’Guérékata G. M.: Almost Automorphic and Almost Periodic Functions in Abstract Spaces, Kluwer Academic/Plenum Publishers, New York, 2001.10.1007/978-1-4757-4482-8Suche in Google Scholar

[32] Sharma P. L.—Anki ReddyK. C.—FunakosiS.: Remarks on uniform space valued almost periodic functions depending on parameters, Math. Sem. Notes Kobe Univ. 4 (1976), 87–90.Suche in Google Scholar

[33] Tornehave H.: On almost periodic movements, Danske Vid. Selsk. Mat.-Fys. Medd. 28 (1954), No. 13, 1–42.Suche in Google Scholar

[34] Tornehave H.: Recent investigations on almost periodic movements. In: Tolfte Skandinaviska Matematikerkongressen, Lund, 1953, Lunds Universitets Matematiska Institution, Lund, 1954, pp. 302–309.Suche in Google Scholar

[35] Veselý M.: Almost periodic homogeneous linear difference systems without almost periodic solutions, J. Difference Equ. Appl. 18 (2012), 1623–1647.10.1080/10236198.2011.585984Suche in Google Scholar

[36] Veselý M.: Almost periodic sequences and functions with given values, Arch. Math. (Brno) 47 (2011), 1–16.Suche in Google Scholar

[37] Veselý M.: Construction of almost periodic functions with given properties, Electron. J. Differential Equations 2011 (2011), No. 29, 1–25.Suche in Google Scholar

[38] Veselý M.: Construction of almost periodic sequences with given properties, Electron. J. Differential Equations 2008 (2008), No. 126, 1–22.Suche in Google Scholar

[39] Zaidman S.: Almost-periodic Functions in Abstract Spaces . Res. Notes Math. 126, Pitman Advanced Publishing Program, Boston, 1985.Suche in Google Scholar

[40] Zhang C.: Almost Periodic Type Functions and Ergodicity, Science Press Beijing/Kluwer Academic Publishers, Beijing/Dordrecht, 2003.10.1007/978-94-007-1073-3Suche in Google Scholar

Received: 2012-10-8
Accepted: 2013-4-19
Published Online: 2016-5-2
Published in Print: 2016-2-1

© 2016 Mathematical Institute Slovak Academy of Sciences

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https://doi.org/10.1515/ms-2015-0114
Schlagwörter für diesen Artikel
limit periodic sequences; limit periodic functions; almost periodicity; asymptotic almost periodicity

Artikel in diesem Heft

  1. Research Article
  2. Prof. RNDr. Ján Jakubík, DrSc. passed away
  3. Research Article
  4. On the number of slim, semimodular lattices
  5. Research Article
  6. Quantum computational algebra with a non-commutative generalization
  7. Research Article
  8. Lexico groups and direct products of lattice ordered groups
  9. Research Article
  10. Values of limit periodic sequences and functions
  11. Research Article
  12. On representation of quasi-Hopf group coalgebras
  13. Research Article
  14. On the q-Bernstein polynomials of the logarithmic function in the case q > 1
  15. Research Article
  16. On some modification of Darboux property
  17. Research Article
  18. Separating sets by peripherally continuous functions
  19. Research Article
  20. Persistence and extinction of a stochastic delay predator-prey model in a polluted environment
  21. Research Article
  22. On O’Malley preponderantly continuous functions
  23. Research Article
  24. Inequalities for the normalized Jensen functional with applications
  25. Research Article
  26. Majorization of starlike and convex functions of complex order involving linear operators
  27. Research Article
  28. Fekete–Szegö problem for some starlike functions related to shell-like curves
  29. Research Article
  30. Central functions for classes of concave univalent functions
  31. Research Article
  32. Inclusion properties for classes of analytic functions associated with conic domains
  33. Research Article
  34. Uniqueness of meromorphic functions and nonlinear differential polynomials sharing a nonzero polynomial
  35. Research Article
  36. Solutions and constrained null-controllability for a differential-difference equation
  37. Research Article
  38. Oscillation criteria for quasi-linear neutral delay dynamic equations on time scale
  39. Research Article
  40. Time periodic solutions for a sixth order nonlinear parabolic equation
  41. Research Article
  42. Some inequalities of trigonometric approximation in weighted Orlicz spaces
  43. Research Article
  44. Summation methods applied to Voronovskaya-type theorems for the partial sums of Fourier series and for Fejér operators
  45. Research Article
  46. Dichotomies for Orlicz spaces
  47. Research Article
  48. On freely generated semigraph C*-algebras
  49. Research Article
  50. Operators with a given part of the numerical range
  51. Research Article
  52. Characterization of quasi-continuity of multifunctions of two variables
  53. Research Paper
  54. Confidence regions in singular weakly nonlinear regression models with constraints
  55. Research Article
  56. Global stability of an SEI model for plant diseases
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