Quasi-Almost Lacunary Statistical Convergence of Sequences of Sets

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Esra Gulle
Ugur Ulusu

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 Cesà ro-type summability spaces, Proc. London Math. Soc. 37 (3) (1978), 508-520.
  2. D. Hajdukovi ´ c, Almost convergence of vector sequences, Mat. Vesnik 12 (27) (1975), 245-249.
  3. D. Hajdukovi ´ c, Quasi-almost convergence in a normed space, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. 13 (2002), 36-41.
  4. E. Gülle and U. Ulusu, Quasi-almost convergence of sequences of sets, J. Inequal. Spec. Funct. (in press).
  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.
  6. F. Nuray and B.E. Rhoades, Statistical convergence of sequences of sets, Fasc. Math. 49 (2012), 87-99.
  7. G. Beer, On convergence of closed sets in a metric space and distance functions, Bull. Aust. Math. Soc. 31 (1985), 421-432.
  8. G. Beer, Wijsman convergence: A survey, Set-Valued Anal. 2 (1994), 77-94.
  9. G. G. Lorentz, A contribution to the theory of divergent sequences, Acta Math. 80 (1948), 167-190.
  10. H. Fast, Sur la convergence statistique, Colloq. Math. 2 (1951), 241-244.
  11. I. J. Maddox, A new type of convergence, Math. Proc. Cambridge Philos. Soc. 83 (1978), 61-64.
  12. J. A. Fridy, On statistical convergence, Analysis 5 (1985), 301-313.
  13. J. A. Fridy and C. Orhan, Lacunary Statistical Convergence, Pac. J. Math. 160 (1) (1993), 43-53.
  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.
  15. R. A. Wijsman, Convergence of sequences of convex sets, cones and functions, Bull. Amer. Math. Soc. 70 (1964), 186-188.
  16. R. A. Wijsman, Convergence of sequences of convex sets, cones and functions II, Trans. Amer. Math. Soc. 123 (1) (1966), 32-45.
  17. T. ˇ Salát, On statistically convergent sequences of real numbers, Math. Slovaca 30 (1980), 139-150.
  18. U. Ulusu, On almost asymptotically lacunary statistical equivalence of sequences of sets, Electr. J. Math. Anal. Appl. 2 (2) (2014), 56-66.
  19. U. Ulusu, Lacunary statistical convergence of sequences of sets, Ph.D. Thesis, Afyon Kocatepe University, Institue of Science and Technology (2013).
  20. U. Ulusu and F. Nuray, On strongly lacunary summability of sequences of sets, J. Appl. Math. Bioinf. 3 (3) (2013), 75-88.
  21. U. Ulusu and F. Nuray, Lacunary Statistical Convergence of Sequences of Sets, Progr. Appl. Math. 4 (2) (2012), 99-109.