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On $\rho -$ Statistical convergence of sequences of Sets

Year 2020, Volume: 3 Issue: 1, 156 - 159, 15.12.2020

Nazlım Deniz Aral , Hacer Şengül Kandemir , Mikail Et

Abstract

In this paper we introduce the concepts of Wijsman $\rho-$statistical convergence, Wijsman strongly $\rho-$statistical convergence and Wijsman $\rho-$strongly $p-$ summability. Also, the relationship between these concepts are given. \newline\newline \textbf{Keywords:} Ces\`{a}ro summability, Statistical convergence, Strongly $p-$Ces\`{a}ro summability, Wijsman convergence.

Keywords

Cesaro summability Statistical convergence Strongly p-Cesaro summability Wijsman convergence

References

  • 1 H. Altınok, M. Et, R. Çolak, Some remarks on generalized sequence space of bounded variation of sequences of fuzzy numbers, Iran. J. Fuzzy Syst. 11(5) (2014), 39–46.
  • 2 V. K. Bhardwaj, S. Dhawan, f-statistical convergence of order $\alpha $ and strong Cesàro summability of order $\alpha $ with respect to a modulus, J. Inequal. Appl. 332 (2015), 14 pp.
  • 3 A. Caserta, G. Di Maio, L. D. R. Kocinac, Statistical convergence in function spaces, Abstr. Appl. Anal., (2011), Article ID 420419, 11 pp.
  • 4 J. S. Connor, The Statistical and strong p-Cesàro convergence of sequences, Analysis 8 (1988), 47–63.
  • 5 H. Çakallı, Lacunary statistical convergence in topological groups, Indian J. Pure Appl. Math. 26(2) (1995), 113–119.
  • 6 H. Çakallı , B. Hazarika, Ideal quasi-Cauchy sequences, J. Inequal. Appl. 234 (2012), 11 pp.
  • 7 H. Çakallı, A variation on ward continuity, Filomat 27(8) (2013), 1545–1549.
  • 8 H. Çakallı, A variation on statistical ward continuity, Bull. Malays. Math. Sci. Soc. 40 (2017), 1701-1710.
  • 9 M. Çınar, M. Karaka¸s, M. Et, On pointwise and uniform statistical convergence of order $\alpha $ for sequences of functions, Fixed Point Theory Appl. 33 (2013), 11 pp.
  • 10 R. Çolak, Statistical convergence of order $\alpha $, Modern Methods in Analysis and Its Applications, New Delhi, India: Anamaya Pub. 2010 (2010) 121–129.
  • 11 R. Çolak, On $\lambda $-Statisitical Convergence, Conference on Summability and Applications, (2011) Istanbul Commerce Univ. May 12-13, ˙Istanbul.
  • 12 M. Et, A. Alotaibi, S. A. Mohiuddine, On $(\Delta ^{m},I)-$ statistical convergence of order $\alpha$, The Scientific World Journal, (2014), Article ID 535419, 5 pages.
  • 13 M. Et, H. ¸ Sengül, Some Cesaro-type summability spaces of order $\alpha$ and lacunary statistical convergence of order $\alpha$, Filomat, 28(8), (2014), 1593–1602.
  • 14 M. Et, B. C. Tripathy, A. J. Dutta, On pointwise statistical convergence of order $\alpha$ of sequences of fuzzy mappings, Kuwait J. Sci. 41(3) (2014), 17–30.
  • 15 M. Et, R. Çolak, Y. Altın, Strongly almost summable sequences of order $\alpha$, Kuwait J. Sci. 41(2) (2014), 35–47.
  • 16 H. Fast, Sur la convergence statistique, Colloq. Math. 2 (1951), 241–244.
  • 17 J. A. Fridy, On statistical convergence, Analysis 5 (1985), 301–313.
  • 18 A. D. Gadjiev, C. Orhan, Some approximation theorems via statistical convergence, Rocky Mountain J. Math. 32(1) (2002), 129–138.
  • 19 M. Işık, K. E. Akbaş, On $\lambda -$statistical convergence of order $\alpha $ in probability, J. Inequal. Spec. Funct. 8(4) (2017), 57–64.
  • 20 F. Nuray, B. E. Rhoades, Statistical convergence of sequences of sets, Fasc. Math. 49 (2012), 87–99.
  • 21 T. Šalát, On statistically convergent sequences of real numbers, Math. Slovaca 30 (1980), 139–150.
  • 22 E. Savaş, M. Et, On $(\Delta _{\lambda }^{m},I)-$\statistical convergence of order $\alpha $, Period. Math. Hungar. 71(2) (2015), 135–145.
  • 23 I. J. Schoenberg, The integrability of certain functions and related summability methods, Amer. Math. Monthly 66 (1959), 361–375.
  • 24 H. Steinhaus, Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math. 2 (1951), 73–74.
  • 25 H. Şengül, Some Cesàro-type summability spaces defined by a modulus function of order $\left( \alpha ,\beta \right) $, Commun. Fac. Sci. Univ. Ank. Sér. A1 Math. Stat. 66(2) (2017), 80–90.
  • 26 U. Ulusu, F. Nuray, Lacunary statistical convergence of sequence of sets, Prog. Appl. Math. 4(2) (2012), 99–109.
  • 27 U. Ulusu, E. Dündar, I-lacunary statistical convergence of sequences of sets, Filomat 28(8) (2014), 1567–1574.

Year 2020, Volume: 3 Issue: 1, 156 - 159, 15.12.2020

Nazlım Deniz Aral , Hacer Şengül Kandemir , Mikail Et

Abstract

References

  • 1 H. Altınok, M. Et, R. Çolak, Some remarks on generalized sequence space of bounded variation of sequences of fuzzy numbers, Iran. J. Fuzzy Syst. 11(5) (2014), 39–46.
  • 2 V. K. Bhardwaj, S. Dhawan, f-statistical convergence of order $\alpha $ and strong Cesàro summability of order $\alpha $ with respect to a modulus, J. Inequal. Appl. 332 (2015), 14 pp.
  • 3 A. Caserta, G. Di Maio, L. D. R. Kocinac, Statistical convergence in function spaces, Abstr. Appl. Anal., (2011), Article ID 420419, 11 pp.
  • 4 J. S. Connor, The Statistical and strong p-Cesàro convergence of sequences, Analysis 8 (1988), 47–63.
  • 5 H. Çakallı, Lacunary statistical convergence in topological groups, Indian J. Pure Appl. Math. 26(2) (1995), 113–119.
  • 6 H. Çakallı , B. Hazarika, Ideal quasi-Cauchy sequences, J. Inequal. Appl. 234 (2012), 11 pp.
  • 7 H. Çakallı, A variation on ward continuity, Filomat 27(8) (2013), 1545–1549.
  • 8 H. Çakallı, A variation on statistical ward continuity, Bull. Malays. Math. Sci. Soc. 40 (2017), 1701-1710.
  • 9 M. Çınar, M. Karaka¸s, M. Et, On pointwise and uniform statistical convergence of order $\alpha $ for sequences of functions, Fixed Point Theory Appl. 33 (2013), 11 pp.
  • 10 R. Çolak, Statistical convergence of order $\alpha $, Modern Methods in Analysis and Its Applications, New Delhi, India: Anamaya Pub. 2010 (2010) 121–129.
  • 11 R. Çolak, On $\lambda $-Statisitical Convergence, Conference on Summability and Applications, (2011) Istanbul Commerce Univ. May 12-13, ˙Istanbul.
  • 12 M. Et, A. Alotaibi, S. A. Mohiuddine, On $(\Delta ^{m},I)-$ statistical convergence of order $\alpha$, The Scientific World Journal, (2014), Article ID 535419, 5 pages.
  • 13 M. Et, H. ¸ Sengül, Some Cesaro-type summability spaces of order $\alpha$ and lacunary statistical convergence of order $\alpha$, Filomat, 28(8), (2014), 1593–1602.
  • 14 M. Et, B. C. Tripathy, A. J. Dutta, On pointwise statistical convergence of order $\alpha$ of sequences of fuzzy mappings, Kuwait J. Sci. 41(3) (2014), 17–30.
  • 15 M. Et, R. Çolak, Y. Altın, Strongly almost summable sequences of order $\alpha$, Kuwait J. Sci. 41(2) (2014), 35–47.
  • 16 H. Fast, Sur la convergence statistique, Colloq. Math. 2 (1951), 241–244.
  • 17 J. A. Fridy, On statistical convergence, Analysis 5 (1985), 301–313.
  • 18 A. D. Gadjiev, C. Orhan, Some approximation theorems via statistical convergence, Rocky Mountain J. Math. 32(1) (2002), 129–138.
  • 19 M. Işık, K. E. Akbaş, On $\lambda -$statistical convergence of order $\alpha $ in probability, J. Inequal. Spec. Funct. 8(4) (2017), 57–64.
  • 20 F. Nuray, B. E. Rhoades, Statistical convergence of sequences of sets, Fasc. Math. 49 (2012), 87–99.
  • 21 T. Šalát, On statistically convergent sequences of real numbers, Math. Slovaca 30 (1980), 139–150.
  • 22 E. Savaş, M. Et, On $(\Delta _{\lambda }^{m},I)-$\statistical convergence of order $\alpha $, Period. Math. Hungar. 71(2) (2015), 135–145.
  • 23 I. J. Schoenberg, The integrability of certain functions and related summability methods, Amer. Math. Monthly 66 (1959), 361–375.
  • 24 H. Steinhaus, Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math. 2 (1951), 73–74.
  • 25 H. Şengül, Some Cesàro-type summability spaces defined by a modulus function of order $\left( \alpha ,\beta \right) $, Commun. Fac. Sci. Univ. Ank. Sér. A1 Math. Stat. 66(2) (2017), 80–90.
  • 26 U. Ulusu, F. Nuray, Lacunary statistical convergence of sequence of sets, Prog. Appl. Math. 4(2) (2012), 99–109.
  • 27 U. Ulusu, E. Dündar, I-lacunary statistical convergence of sequences of sets, Filomat 28(8) (2014), 1567–1574.
There are 27 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Nazlım Deniz Aral

Hacer Şengül Kandemir 0000-0003-4453-0786

Mikail Et

Publication Date December 15, 2020
Acceptance Date October 1, 2020
Published in Issue Year 2020 Volume: 3 Issue: 1

Cite

APA Aral, N. D., Şengül Kandemir, H., & Et, M. (2020). On $\rho -$ Statistical convergence of sequences of Sets. Conference Proceedings of Science and Technology, 3(1), 156-159.
AMA Aral ND, Şengül Kandemir H, Et M. On $\rho -$ Statistical convergence of sequences of Sets. Conference Proceedings of Science and Technology. December 2020;3(1):156-159.
Chicago Aral, Nazlım Deniz, Hacer Şengül Kandemir, and Mikail Et. “On $\rho -$ Statistical Convergence of Sequences of Sets”. Conference Proceedings of Science and Technology 3, no. 1 (December 2020): 156-59.
EndNote Aral ND, Şengül Kandemir H, Et M (December 1, 2020) On $\rho -$ Statistical convergence of sequences of Sets. Conference Proceedings of Science and Technology 3 1 156–159.
IEEE N. D. Aral, H. Şengül Kandemir, and M. Et, “On $\rho -$ Statistical convergence of sequences of Sets”, Conference Proceedings of Science and Technology, vol. 3, no. 1, pp. 156–159, 2020.
ISNAD Aral, Nazlım Deniz et al. “On $\rho -$ Statistical Convergence of Sequences of Sets”. Conference Proceedings of Science and Technology 3/1 (December 2020), 156-159.
JAMA Aral ND, Şengül Kandemir H, Et M. On $\rho -$ Statistical convergence of sequences of Sets. Conference Proceedings of Science and Technology. 2020;3:156–159.
MLA Aral, Nazlım Deniz et al. “On $\rho -$ Statistical Convergence of Sequences of Sets”. Conference Proceedings of Science and Technology, vol. 3, no. 1, 2020, pp. 156-9.
Vancouver Aral ND, Şengül Kandemir H, Et M. On $\rho -$ Statistical convergence of sequences of Sets. Conference Proceedings of Science and Technology. 2020;3(1):156-9.
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