Title: On I-Asymptotically Lacunary Statistical Equivalence of Functions on Amenable Semigroups
Author(s): Ömer Kişi, Burak Çakal
Pages: 14-25
Cite as:
Ömer Kişi, Burak Çakal, On I-Asymptotically Lacunary Statistical Equivalence of Functions on Amenable Semigroups, Int. J. Anal. Appl., 17 (1) (2019), 14-25.


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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  1. M. Day, Amenable semigroups, Illinois J. Math. 1 (1957), 509–544. Google Scholar

  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. Google Scholar

  3. S.A. Douglass, On a concept of summability in amenable semigroups, Math. Scand. 28 (1968), 96-102. Google Scholar

  4. S.A. Douglass, Summing sequences for amenable semigroups, Michigan Math. J. 20 (1973), 169-179. Google Scholar

  5. H. Fast, Sur la convergence statistique, Colloq. Math. 2 (1951), 241–244. Google Scholar

  6. J. A Fridy and Orhan C., Lacunary Statistical Convergence, Pacific J. Math., 160(1) (1993), 43-51. Google Scholar

  7. A.R. Freedman, J.J. Sember and M. Raphael, Some Ces`aro type summability spaces, Proc. Lond. Math. Soc., 37 (1978), 508-520. Google Scholar

  8. P. Kostyrko, T. Sal´at and W. Wilezy´nski, I-Convergence, Real Anal. Exchange, 26(2) (2000), 669-686. Google Scholar

  9. M. Marouf, Asymptotic equivalence and summability, Internat. J. Math. Math. Sci., 16(4) (1993), 755-762. Google Scholar

  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, Kır¸sehir, Turkey (2018), 104-110. Google Scholar

  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. Google Scholar

  12. O. Ki¸si and B. C¸ akal, On ¨ Iσ-convergence of folner sequence on amenable semigroups, NTMSCI 6(2) (2018), 222-235. Google Scholar

  13. P.F. Mah, Summability in amenable semigroups, Trans. Amer. Math. Soc. 156 (1971), 391–403. Google Scholar

  14. P.F. Mah, Matrix summability in amenable semigroups, Proc. Amer. Math. Soc. 36 (1972), 414–420. Google Scholar

  15. M. Mursaleen, λ-Statistical Convergence, Math. Slovaca, 50(1) (2000), 111-115. Google Scholar

  16. R.F. Patterson, On asymptotically statistically equivalent sequences, Demostratio Math., 36(1) (2003), 149-153. Google Scholar

  17. R.F. Patterson and E. Sava¸s, On asymptotically lacunary statistical equivalent sequences, Thai J. Math., 4(2) (2006), 267-272. Google Scholar

  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. Google Scholar

  19. E. Sava¸s and P. Das, A generalized statistical convergence via ideals, Appl. Math. Lett., 24 (2011), 826–830. Google Scholar

  20. E. Sava¸s, On I-asymptotically lacunary statistical equivalent sequences, Adv. Difference Equ., 2013 (2013), Art. ID 111. Google Scholar

  21. F. Nuray and B.E. Rhoades, Some kinds of convergence defined by Folner sequences, Analysis, 31(4) (2011), 381–390. Google Scholar

  22. F. Nuray and B.E. Rhoades, Asymptotically and Statistically Equivalent Functions Defined on Amenable Semigroups, Thai J. Math., 11(2) (2013), 303–311. Google Scholar

  23. I. Nomika, Folner’s conditions for amenable semigroups, Math. Scand., 15 (1964), 18–28. Google Scholar

  24. I.J. Schoenberg, The integrability of certain functions and related summability methods, Amer. Math. Monthly, 66 (1959), 361-375. Google Scholar


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