On I-Asymptotically Lacunary Statistical Equivalence of Functions on Amenable Semigroups

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Ömer Kişi, Burak Çakal

Abstract

In this study we define the notions of asymptotically paper, we introduce the concept of Iasymptotically statistical equivalent and I-asymptotically lacunary statistical equivalent functions defined on discrete countable amenable semigroups. In addition to these definitions, we give some inclusion theorems.

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References

  1. M. Day, Amenable semigroups, Illinois J. Math. 1 (1957), 509-544.
  2. P. Das, E. Sava ¸s and S. Kr. Ghosal, On generalized of certain summability methods using ideals, Appl. Math. Letter, 36 (2011), 1509-1514.
  3. S.A. Douglass, On a concept of summability in amenable semigroups, Math. Scand. 28 (1968), 96-102.
  4. S.A. Douglass, Summing sequences for amenable semigroups, Michigan Math. J. 20 (1973), 169-179.
  5. H. Fast, Sur la convergence statistique, Colloq. Math. 2 (1951), 241-244.
  6. J. A Fridy and Orhan C., Lacunary Statistical Convergence, Pacific J. Math., 160(1) (1993), 43-51.
  7. A.R. Freedman, J.J. Sember and M. Raphael, Some Ces`aro type summability spaces, Proc. Lond. Math. Soc., 37 (1978), 508-520.
  8. P. Kostyrko, T. Sal ´at and W. Wilezy ´nski, I-Convergence, Real Anal. Exchange, 26(2) (2000), 669-686.
  9. M. Marouf, Asymptotic equivalence and summability, Internat. J. Math. Math. Sci., 16(4) (1993), 755-762.
  10. O. Ki ¸si and E. G ¨uler, A generalized statistical convergence via ideals defined by folner sequence on amenable semigroup, ¨ In Prooceding of 4th International Conference on Analysis and its Applications, Kir ¸sehir, Turkey (2018), 104-110.
  11. O. Ki ¸si and E. G ¨uler, ¨ σ-asymptotically lacunary statistical equivalent functions on amenable semigroups, Far East J. Appl. Math., 97(6) (2017), 275-287.
  12. O. Ki ¸si and B. C ¸ akal, On ¨ Iσ-convergence of folner sequence on amenable semigroups, NTMSCI 6(2) (2018), 222-235.
  13. P.F. Mah, Summability in amenable semigroups, Trans. Amer. Math. Soc. 156 (1971), 391-403.
  14. P.F. Mah, Matrix summability in amenable semigroups, Proc. Amer. Math. Soc. 36 (1972), 414-420.
  15. M. Mursaleen, λ-Statistical Convergence, Math. Slovaca, 50(1) (2000), 111-115.
  16. R.F. Patterson, On asymptotically statistically equivalent sequences, Demostratio Math., 36(1) (2003), 149-153.
  17. R.F. Patterson and E. Sava ¸s, On asymptotically lacunary statistical equivalent sequences, Thai J. Math., 4(2) (2006), 267-272.
  18. I.P. Pobyvanets, Asymptotic equivalence of some linear transformations defined by a nonnegative matrix and reduced to generalized equivalence in the sense of Ces`aro and Abel, Mat. Fiz. no. 28 (1980), 83-87.
  19. E. Sava ¸s and P. Das, A generalized statistical convergence via ideals, Appl. Math. Lett., 24 (2011), 826-830.
  20. E. Sava ¸s, On I-asymptotically lacunary statistical equivalent sequences, Adv. Difference Equ., 2013 (2013), Art. ID 111.
  21. F. Nuray and B.E. Rhoades, Some kinds of convergence defined by Folner sequences, Analysis, 31(4) (2011), 381-390.
  22. F. Nuray and B.E. Rhoades, Asymptotically and Statistically Equivalent Functions Defined on Amenable Semigroups, Thai J. Math., 11(2) (2013), 303-311.
  23. I. Nomika, Folner's conditions for amenable semigroups, Math. Scand., 15 (1964), 18-28.
  24. I.J. Schoenberg, The integrability of certain functions and related summability methods, Amer. Math. Monthly, 66 (1959), 361-375.