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Year 2020, Volume: 8 Issue: 2, 322 - 328, 27.10.2020

Abstract

References

  • [1] Baronti, M. and Papini, P., Convergence of sequences of sets, In: Methods of Functional Analysis in Approximation Theory (pp. 133–155), Birkh¨auser, Basel, 1986.
  • [2] G. Beer, On convergence of closed sets in a metric space and distance functions, Bull. Aust. Math. Soc. 31 (1985), 421–432.
  • [3] G. Beer, Wijsman convergence: A survey, Set-Valued Analysis 2(1-2) (1994), 77–94.
  • [4] J.S. Connor, The statistical and strong p-Cesaro convergence of sequences, Analysis 8(1-2) (1988), 47–64.
  • [5] M. Et and H. Sengul, On (Dm; I)-lacunary statistical convergence of order a, J. Math. Anal. 7(5) (2016), 78–84.
  • [6] H. Fast, Sur la convergence statistique, Colloq. Math. 2(3-4) (1951), 241–244.
  • [7] J.A. Fridy, On statistical convergence, Analysis 5(4) (1985), 301–314.
  • [8] J.A. Fridy and C. Orhan, Lacunary statistical convergence, Pacific Journal of Mathematics 160(1) (1993), 43–51.
  • [9] E. G¨ulle and U. Ulusu, Wijsman quasi-invariant convergence, Creat. Math. Inform. 28(2) (2019), 113–120.
  • [10] D. Hajdukovic, Quasi-almost convergence in a normed space, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. 13 (2002), 36–41.
  • [11] M. Mursaleen, Invariant mean and some matrix transformations, Thamkang J. Math. 10 (1979), 183–188.
  • [12] M. Mursaleen, On some new invariant matrix methods of summability, Quart. J. Math. Oxford 34(2) (1983), 77–86.
  • [13] M. Mursaleen and O.H.H. Edely, On the invariant mean and statistical convergence, Appl. Math. Lett. 22(11) (2009), 1700–1704.
  • [14] F. Nuray and B.E. Rhoades, Statistical convergence of sequences of sets, Fasc. Math. 49 (2012), 87–99.
  • [15] 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.
  • [16] N. Pancaroglu and F. Nuray, On invariant statistically convergence and lacunary invariant statistical convergence of sequences of sets, Progress in Applied Mathematics 5(2) (2013), 23–29.
  • [17] N. Pancaroglu and F. Nuray, Statistical lacunary invariant summability, Theoretical Mathematics and Applications 3(2) (2013), 71–78.
  • [18] N. Pancaroglu Akın, E. D¨undar and U. Ulusu, Wijsman lacunary I-invariant convergence of sequences of sets, Proc. Nat. Acad. Sci. India Sect. A (accepted).
  • [19] R.A. Raimi, Invariant means and invariant matrix methods of summability, Duke Math. J. 30(1) (1963), 81–94.
  • [20] E. Savas¸, Some sequence spaces involving invariant means, Indian J. Math. 31 (1989), 1–8.
  • [21] E. Savas, On lacunary strong s-convergence, Indian J. Pure Appl. Math. 21 (1990), 359–365.
  • [22] E. Savas and F. Nuray, On s-statistically convergence and lacunary s-statistically convergence, Math. Slovaca 43(3) (1993), 309–315.
  • [23] E. Savas¸, U. Yamancı and M. G¨urdal, I-lacunary statistical convergence of weighted g via modulus functions in 2-normed spaces, Commun. Fac. Sci. Univ. Ank. Ser A1 Math. Stat. 68(2) (2019), 2324–2332.
  • [24] P. Schaefer, Infinite matrices and invariant means, Prog. Amer. Math. Soc. 36(1) (1972), 104–110.
  • [25] T. Salat, On statistically convergent sequences of real numbers, Math. Slovaca 30(2) (1980), 139–150.
  • [26] H. Sengul and M. Et, On lacunary statistical convergence of order a, Acta Math. Sci. Ser. B 34(2) (2014), 473–482.
  • [27] H. Sengul and M. Et, f -lacunary statistical convergence and strong f -lacunary summability of order a, Filomat 32(13) (2018), 4513–4521.
  • [28] U. Ulusu and F. Nuray, Lacunary statistical convergence of sequences of sets, Progress in Applied Mathematics 4(2) (2012), 99–109.
  • [29] U. Ulusu and F. Nuray, On strongly lacunary summability of sequences of sets, Journal of Applied Mathematics and Bioinformatics 3(3) (2013), 75–88.
  • [30] U. Ulusu and E. Dundar, I-lacunary statistical convergence of sequences of sets, Filomat 28(8) (2014), 1567–1574.
  • [31] U. Yamancı and M. Gurdal, On lacunary ideal convergence in random n-normed space, Journal of Mathematics 2013(Article ID 868457) (2013), 8 pages.
  • [32] U. Yamancı and M. Gurdal, I-statistical convergence in 2-normed space, Arab Journal of Mathematical Sciences 20(1) (2014), 41–47.
  • [33] R.A. Wijsman, Convergence of sequences of convex sets, cones and functions, Bull. Amer. Math. Soc. 70(1) (1964), 186–188.
  • [34] R.A. Wijsman, Convergence of sequences of convex sets, cones and functions II, Trans. Amer. Math. Soc. 123(1) (1966), 32–45.

Quasi-Lacunary Invariant Statistical Convergence of Sequences of Sets

Year 2020, Volume: 8 Issue: 2, 322 - 328, 27.10.2020

Abstract

In this study, we give definitions of Wijsman quasi-lacunary invariant convergence, Wijsman quasi-strongly lacunary invariant convergence and Wijsman quasi-strongly $q$-lacunary invariant convergence for sequences of sets. Also we define Wijsman quasi-lacunary invariant statistical convergence. Then, we examine the existence of the relations among these new convergence types and some convergence types for sequences of sets given before. Furthermore, we examine the existence of the relations between some of these new convergence types, too.

References

  • [1] Baronti, M. and Papini, P., Convergence of sequences of sets, In: Methods of Functional Analysis in Approximation Theory (pp. 133–155), Birkh¨auser, Basel, 1986.
  • [2] G. Beer, On convergence of closed sets in a metric space and distance functions, Bull. Aust. Math. Soc. 31 (1985), 421–432.
  • [3] G. Beer, Wijsman convergence: A survey, Set-Valued Analysis 2(1-2) (1994), 77–94.
  • [4] J.S. Connor, The statistical and strong p-Cesaro convergence of sequences, Analysis 8(1-2) (1988), 47–64.
  • [5] M. Et and H. Sengul, On (Dm; I)-lacunary statistical convergence of order a, J. Math. Anal. 7(5) (2016), 78–84.
  • [6] H. Fast, Sur la convergence statistique, Colloq. Math. 2(3-4) (1951), 241–244.
  • [7] J.A. Fridy, On statistical convergence, Analysis 5(4) (1985), 301–314.
  • [8] J.A. Fridy and C. Orhan, Lacunary statistical convergence, Pacific Journal of Mathematics 160(1) (1993), 43–51.
  • [9] E. G¨ulle and U. Ulusu, Wijsman quasi-invariant convergence, Creat. Math. Inform. 28(2) (2019), 113–120.
  • [10] D. Hajdukovic, Quasi-almost convergence in a normed space, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. 13 (2002), 36–41.
  • [11] M. Mursaleen, Invariant mean and some matrix transformations, Thamkang J. Math. 10 (1979), 183–188.
  • [12] M. Mursaleen, On some new invariant matrix methods of summability, Quart. J. Math. Oxford 34(2) (1983), 77–86.
  • [13] M. Mursaleen and O.H.H. Edely, On the invariant mean and statistical convergence, Appl. Math. Lett. 22(11) (2009), 1700–1704.
  • [14] F. Nuray and B.E. Rhoades, Statistical convergence of sequences of sets, Fasc. Math. 49 (2012), 87–99.
  • [15] 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.
  • [16] N. Pancaroglu and F. Nuray, On invariant statistically convergence and lacunary invariant statistical convergence of sequences of sets, Progress in Applied Mathematics 5(2) (2013), 23–29.
  • [17] N. Pancaroglu and F. Nuray, Statistical lacunary invariant summability, Theoretical Mathematics and Applications 3(2) (2013), 71–78.
  • [18] N. Pancaroglu Akın, E. D¨undar and U. Ulusu, Wijsman lacunary I-invariant convergence of sequences of sets, Proc. Nat. Acad. Sci. India Sect. A (accepted).
  • [19] R.A. Raimi, Invariant means and invariant matrix methods of summability, Duke Math. J. 30(1) (1963), 81–94.
  • [20] E. Savas¸, Some sequence spaces involving invariant means, Indian J. Math. 31 (1989), 1–8.
  • [21] E. Savas, On lacunary strong s-convergence, Indian J. Pure Appl. Math. 21 (1990), 359–365.
  • [22] E. Savas and F. Nuray, On s-statistically convergence and lacunary s-statistically convergence, Math. Slovaca 43(3) (1993), 309–315.
  • [23] E. Savas¸, U. Yamancı and M. G¨urdal, I-lacunary statistical convergence of weighted g via modulus functions in 2-normed spaces, Commun. Fac. Sci. Univ. Ank. Ser A1 Math. Stat. 68(2) (2019), 2324–2332.
  • [24] P. Schaefer, Infinite matrices and invariant means, Prog. Amer. Math. Soc. 36(1) (1972), 104–110.
  • [25] T. Salat, On statistically convergent sequences of real numbers, Math. Slovaca 30(2) (1980), 139–150.
  • [26] H. Sengul and M. Et, On lacunary statistical convergence of order a, Acta Math. Sci. Ser. B 34(2) (2014), 473–482.
  • [27] H. Sengul and M. Et, f -lacunary statistical convergence and strong f -lacunary summability of order a, Filomat 32(13) (2018), 4513–4521.
  • [28] U. Ulusu and F. Nuray, Lacunary statistical convergence of sequences of sets, Progress in Applied Mathematics 4(2) (2012), 99–109.
  • [29] U. Ulusu and F. Nuray, On strongly lacunary summability of sequences of sets, Journal of Applied Mathematics and Bioinformatics 3(3) (2013), 75–88.
  • [30] U. Ulusu and E. Dundar, I-lacunary statistical convergence of sequences of sets, Filomat 28(8) (2014), 1567–1574.
  • [31] U. Yamancı and M. Gurdal, On lacunary ideal convergence in random n-normed space, Journal of Mathematics 2013(Article ID 868457) (2013), 8 pages.
  • [32] U. Yamancı and M. Gurdal, I-statistical convergence in 2-normed space, Arab Journal of Mathematical Sciences 20(1) (2014), 41–47.
  • [33] R.A. Wijsman, Convergence of sequences of convex sets, cones and functions, Bull. Amer. Math. Soc. 70(1) (1964), 186–188.
  • [34] R.A. Wijsman, Convergence of sequences of convex sets, cones and functions II, Trans. Amer. Math. Soc. 123(1) (1966), 32–45.
There are 34 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Esra Gülle 0000-0001-5575-2937

Uğur Ulusu 0000-0001-7658-6114

Publication Date October 27, 2020
Submission Date March 29, 2020
Acceptance Date May 28, 2020
Published in Issue Year 2020 Volume: 8 Issue: 2

Cite

APA Gülle, E., & Ulusu, U. (2020). Quasi-Lacunary Invariant Statistical Convergence of Sequences of Sets. Konuralp Journal of Mathematics, 8(2), 322-328.
AMA Gülle E, Ulusu U. Quasi-Lacunary Invariant Statistical Convergence of Sequences of Sets. Konuralp J. Math. October 2020;8(2):322-328.
Chicago Gülle, Esra, and Uğur Ulusu. “Quasi-Lacunary Invariant Statistical Convergence of Sequences of Sets”. Konuralp Journal of Mathematics 8, no. 2 (October 2020): 322-28.
EndNote Gülle E, Ulusu U (October 1, 2020) Quasi-Lacunary Invariant Statistical Convergence of Sequences of Sets. Konuralp Journal of Mathematics 8 2 322–328.
IEEE E. Gülle and U. Ulusu, “Quasi-Lacunary Invariant Statistical Convergence of Sequences of Sets”, Konuralp J. Math., vol. 8, no. 2, pp. 322–328, 2020.
ISNAD Gülle, Esra - Ulusu, Uğur. “Quasi-Lacunary Invariant Statistical Convergence of Sequences of Sets”. Konuralp Journal of Mathematics 8/2 (October 2020), 322-328.
JAMA Gülle E, Ulusu U. Quasi-Lacunary Invariant Statistical Convergence of Sequences of Sets. Konuralp J. Math. 2020;8:322–328.
MLA Gülle, Esra and Uğur Ulusu. “Quasi-Lacunary Invariant Statistical Convergence of Sequences of Sets”. Konuralp Journal of Mathematics, vol. 8, no. 2, 2020, pp. 322-8.
Vancouver Gülle E, Ulusu U. Quasi-Lacunary Invariant Statistical Convergence of Sequences of Sets. Konuralp J. Math. 2020;8(2):322-8.
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