Title: Quasi-Almost Lacunary Statistical Convergence of Sequences of Sets
Author(s): Esra Gulle, Ugur Ulusu
Pages: 222-231
Cite as:
Esra Gulle, Ugur Ulusu, Quasi-Almost Lacunary Statistical Convergence of Sequences of Sets, Int. J. Anal. Appl., 16 (2) (2018), 222-231.

Abstract


In this study, we defined concepts of Wijsman quasi-almost lacunary convergence, Wijsman quasi-strongly almost lacunary convergence and Wijsman quasi q-strongly almost lacunary convergence. Also we give the concept of Wijsman quasi-almost lacunary statistically convergence. Then, we study relationships among these concepts. Furthermore, we investigate relationship between these concepts and some convergences types given earlier for sequences of sets, too.

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References


  1. A. R. Freedman, J. J. Sember and M. Raphael, Some Cesàro-type summability spaces, Proc. London Math. Soc. 37 (3) (1978), 508–520. Google Scholar

  2. D. Hajdukovi´ c, Almost convergence of vector sequences, Mat. Vesnik 12 (27) (1975), 245–249. Google Scholar

  3. D. Hajdukovi´ c, Quasi-almost convergence in a normed space, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. 13 (2002), 36–41. Google Scholar

  4. E. Gülle and U. Ulusu, Quasi-almost convergence of sequences of sets, J. Inequal. Spec. Funct. (in press). Google Scholar

  5. F. Nuray, Quasi-invariant convergence in a normed space, Annals of the University of Craiova, Mathematics and Computer Science Series 41 (1) (2014), 1–5. Google Scholar

  6. F. Nuray and B.E. Rhoades, Statistical convergence of sequences of sets, Fasc. Math. 49 (2012), 87–99. Google Scholar

  7. G. Beer, On convergence of closed sets in a metric space and distance functions, Bull. Aust. Math. Soc. 31 (1985), 421–432. Google Scholar

  8. G. Beer, Wijsman convergence: A survey, Set-Valued Anal. 2 (1994), 77–94. Google Scholar

  9. G. G. Lorentz, A contribution to the theory of divergent sequences, Acta Math. 80 (1948), 167–190. Google Scholar

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

  11. I. J. Maddox, A new type of convergence, Math. Proc. Cambridge Philos. Soc. 83 (1978), 61–64. Google Scholar

  12. J. A. Fridy, On statistical convergence, Analysis 5 (1985), 301–313. Google Scholar

  13. J. A. Fridy and C. Orhan, Lacunary Statistical Convergence, Pac. J. Math. 160 (1) (1993), 43–53. Google Scholar

  14. M. Baronti and P. Papini, Convergence of sequences of sets, In: Methods of functional analysis in approximation theory, ISNM 76, Birkhauser-Verlag, Basel 1986. Google Scholar

  15. R. A. Wijsman, Convergence of sequences of convex sets, cones and functions, Bull. Amer. Math. Soc. 70 (1964), 186–188. Google Scholar

  16. R. A. Wijsman, Convergence of sequences of convex sets, cones and functions II, Trans. Amer. Math. Soc. 123 (1) (1966), 32–45. Google Scholar

  17. T. ˇ Salát, On statistically convergent sequences of real numbers, Math. Slovaca 30 (1980), 139–150. Google Scholar

  18. U. Ulusu, On almost asymptotically lacunary statistical equivalence of sequences of sets, Electr. J. Math. Anal. Appl. 2 (2) (2014), 56–66. Google Scholar

  19. U. Ulusu, Lacunary statistical convergence of sequences of sets, Ph.D. Thesis, Afyon Kocatepe University, Institue of Science and Technology (2013). Google Scholar

  20. U. Ulusu and F. Nuray, On strongly lacunary summability of sequences of sets, J. Appl. Math. Bioinf. 3 (3) (2013), 75–88. Google Scholar

  21. U. Ulusu and F. Nuray, Lacunary Statistical Convergence of Sequences of Sets, Progr. Appl. Math. 4 (2) (2012), 99–109. Google Scholar


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