Quasi-Slowly Oscillating Sequences in Locally Normal Riesz Spaces

Article Sidebar

PDF
Cite as:
Bipan Hazarika, Ayhan Esi, Quasi-Slowly Oscillating Sequences in Locally Normal Riesz Spaces, Int. J. Anal. Appl., 15 (2) (2017), 229-237.

Main Article Content

Bipan Hazarika, Ayhan Esi

Abstract

In this paper, we study quasi-slowly oscillating sequences, on quasi-slowly oscillating compactness and quasi-slowly oscillating continuous functions in locally normal Riesz space.

Article Details

References

  1. H. Albayrak and S. Pehlivan, Statistical convergence and statistical continuity on locally solid Riesz spaces, Topology Appl. 159 (2012), 1887-1893.
  2. C. D. Aliprantis and O. Burkinshaw, Locally Solid Riesz Spaces with Applications to Economics, Second Ed., Amer. Math. Soc., 2003.
  3. A. Alotaibi, B. Hazarika and S. A. Mohiuddine, On the ideal convergence of double sequences in locally solid Riesz spaces, Abst. Appl. Anal. 2014 (2004), Article ID 396254, 6 pages.
  4. D. Burton and J. Coleman, Quasi-Cauchy Sequences, Amer. Math. Monthly 117(4)(2010), 328-333.
  5. H. C ¸akalli and B. Hazarika, Ideal-quasi-Cauchy sequences, J. Inequal. Appl. 2012 (2012), Art. ID 234, 11 pages.
  6. H. C ¸akalli Forward continuity, J. Comput. Anal. Appl. 13(2)(2011), 225-230.
  7. H. C ¸akalli, Statistical ward continuity, Appl. Math. Lett. 24(10)(2011), 1724-1728.
  8. H. C ¸akalli Statistical-quasi-Cauchy sequences, Math. Comput. Modelling 54(5-6)(2011), 1620-1624.
  9. H. C ¸akalli Slowly oscillating continuity, Abst. Appl. Anal. 2008(2008), Article ID 485706, 5 pages.
  10. H. C ¸akalli On G-continuity, Comput. Math. Appl. 61(2011), 313-318.
  11. H. C ¸akalli Delta quasi-Cauchy sequences, Math. Comput. Modelling 53(2011), 397-401.
  12. H. C ¸akalli and A. Sönmez, Slowly oscillating continuity in abstract metric spaces, Filomat 27(5)(2013), 925-930.
  13. J. Connor and K. G. Grosse-Erdmann, Sequential definitions of continuity for real functions, Rocky Mountain J. Math. 33(1)(2003), 93-121.
  14. H. C ¸akalli I. C ¸anak and M. Dik, ∆-quasi-slowly oscillating continuity. Appl. Math. Comput. 216(10)(2010), 2865- 2868.
  15. M. Dik and I. C ¸anak, New Types of Continuities, Abst. Appl. Anal. 2010(2010), Article ID 258980, 6 pages.
  16. H. Fast, Sur la convergence statistique, Colloq. Math. 2(1951), 241-244.
  17. A. R. Freedman, J. J. Sember and M. Raphael, Some Cesaro-type summability spaces, Proc. London Math. Soc. 3(37)(1978), 508-520.
  18. J. A. Fridy, On statistical convergence, Analysis 5(1985), 301-313.
  19. J. A. Fridy and C. Orhan, Lacunary statistical convergence, Pacific J. Math. 160(1)(1993), 43-51.
  20. J. A. Fridy and C. Orhan, Lacunary statistical summability, J. Math. Anal. Appl. 173(1993), 497-504.
  21. B. Hazarika, Ideal convergence in locally solid Riesz spaces, Filomat 28(4)(2014), 797-809.
  22. B. Hazarika, Second order ideal-ward continuity, Int. J. Anal. 2014(2014), Article ID 480918, 4 pages.
  23. B. Hazarika, S. A. Mohiuddine and M. Mursaleen, Lacunary density and some inclusion results in locally solid Riesz spaces, Iranian J. Sci. Tech., Transactions-A, 38A1 (2014), 61-68
  24. B. Hazarika, M. Kemal Ozdemir and A. Esi, Slowly Oscillating Sequences in Locally Normal Riesz Spaces, Int. J. Adv. Appl. Sci. 4(1)(2017), 96-101.
  25. L. V. Kantorovich, Lineare halbgeordnete Raume, Rec. Math. 2 (1937), 121-168.
  26. P. Kostyrko, T. ˘ Salát and W. Wilczy ´ nski, I-convergence, Real Anal. Exch. 26(2)(2000-2001), 669-686.
  27. W. A. J. Luxemburg and A. C. Zaanen, Riesz Spaces I, North-Holland, Amsterdam, 1971.
  28. S. A. Mohiuddine, A. Alotaibi and M. Mursaleen, Statistical convergence of double sequences in locally solid Riesz spaces, Abst. Appl. Anal. 2012(2012), Article ID 719729, 9 pages.
  29. S. A. Mohiuddine and M. A. Alghamdi, Statistical summability through lacunary sequence in locally solid Riesz spaces, J. Inequal. Appl. 2012(2012), Article ID 225, 9 pages.
  30. S. A. Mohiuddine, A. Alotaibi and M. Mursaleen, Statistical convergence of double sequences in locally solid Riesz spaces, Abst. Appl. Anal. 2012(2012), Article ID 719729, 9 pages.
  31. S. A. Mohiuddine, B. Hazarika and A. Alotaibi, Double lacunary density and some inclusion results in locally solid Riesz spaces, Abst. Appl. Anal. 2013(2013), Article ID 507962, 8 pages.
  32. F. Riesz, Sur la d ´ ecomposition des op ´ erations fonctionelles lin ´ eaires, in: Atti del Congr. Internaz. dei Mat., 3, Bologna, 1928, Zanichelli, 1930, 143-148.
  33. G. T. Roberts, Topologies in vector lattices, Math. Proc. Camb. Phil. Soc. 48 (1952), 533-546.
  34. H. Steinhaus, Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math. 2 (1951), 73-74.
  35. R. W. Vallin, Creating slowly oscillating sequences and slowly oscillating continuous functions, With an appendix by Vallin and Cakalli, Acta Math. Univ. Comenian(N.S.) 80(1)(2011), 71-78.
  36. A. C. Zannen, Introduction to Operator Theory in Riesz Spaces, Springer-Verlag, 1997.
  37. A. Zygmund, Trigonometrical Series, vol. 5 of Monograf ´ yas de Matemáticas, Warszawa-Lwow, 1935.
  38. A. Zygmund, Trigonometric Series, Cambridge University Press, Cambridge, UK, 2nd edition, 1979.