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Invariant and Lacunary Invariant Statistical Convergence of Order $\eta$ for Double Set Sequences

Year 2022, Volume: 7 Issue: 1, 14 - 20, 30.04.2022

Abstract

In this study, for double set sequences, we introduced the notions of invariant and lacunary invariant statistical convergence of order $\eta$ ($0<\eta\leq 1$) in the Wijsman sense. Also, we investigated the inclusion relations between them.

References

  • M. Baronti and P. Papini, Convergence of sequences of sets, In: Methods of Functional Analysis in Approximation Theory (pp.133-155), Birkhäuser, Basel, (1986).
  • G. Beer, Wijsman convergence: A survey, Set-Valued Anal., 2(1) (1994), 77-94.
  • R. Çolak, Statistical convergence of order α, In: Modern Methods in Analysis and Its Applications (pp.121-129), Anamaya Publishers, New Delhi, (2010).
  • E. Gülle and U. Ulusu, Double Wijsman lacunary statistical convergence of order α, J. Appl. Math. Inform., 39(3-4) (2021), 303-319.
  • M. Mursaleen and O.H.H. Edely, Statistical convergence of double sequences, J. Math. Anal. Appl., 288(1) (2003), 223-231.
  • F. Nuray and B.E. Rhoades, Statistical convergence of sequences of sets, Fasc. Math., 49 (2012), 87-99.
  • F. Nuray, U. Ulusu and E. Dündar, Lacunary statistical convergence of double sequences of sets, Soft Comput., 20(7) (2016), 2883-2888.
  • F. Nuray and U. Ulusu, Lacunary invariant statistical convergence of double sequences of sets, Creat. Math. Inform., 28(2) (2019), 143-150.
  • F. Nuray, E. Dündar and U. Ulusu, Wijsman statistical convergence of double sequences of sets, Iran. J. Math. Sci. Inform., 16(1) (2021), 55-64.
  • N. Pancarog ̆lu and F. Nuray, On invariant statistically convergence and lacunary invariant statistical convergence of sequences of sets, Progress Appl. Math., 5(2) (2013), 23-29.
  • R.F. Patterson and E. Savaş, Lacunary statistical convergence of double sequences, Math. Commun., 10(1) (2005), 55-61.
  • A. Pringsheim, Zur theorie der zweifach unendlichen Zahlenfolgen, Math. Ann., 53(3) (1900), 289-321.
  • E. Savaş and R.F. Patterson, Double σ-convergence lacunary statistical sequences, J. Comput. Anal. Appl., 11(4) (2009), 610-615.
  • E. Savaş, Double almost statistical convergence of order α, Adv. Difference Equ., 2013(62) (2013), 9 pages.
  • E. Savaş, Double almost lacunary statistical convergence of order α, Adv. Difference Equ., 2013(254) (2013), 10 pages.
  • E. Savaş, On I-lacunary statistical convergence of order α for sequences of sets, Filomat, 29(6) (2015), 1223-1229.
  • H. Şengül and M. Et, On lacunary statistical convergence of order α, Acta Math. Sci. Ser. B, 34(2) (2014), 473-482.
  • H. Şengül and M. Et, On I-lacunary statistical convergence of order α of sequences of sets, Filomat, 31(8) (2017), 2403-2412.
  • U. Ulusu and F. Nuray, Lacunary statistical convergence of sequences of sets, Progress Appl. Math., 4(2) (2012), 99-109.
  • U. Ulusu and E. Gülle, Some statistical convergence types of order α for double set sequences, Facta Univ. Ser. Math. Inform., 35(3) (2020), 595-603.
Year 2022, Volume: 7 Issue: 1, 14 - 20, 30.04.2022

Abstract

References

  • M. Baronti and P. Papini, Convergence of sequences of sets, In: Methods of Functional Analysis in Approximation Theory (pp.133-155), Birkhäuser, Basel, (1986).
  • G. Beer, Wijsman convergence: A survey, Set-Valued Anal., 2(1) (1994), 77-94.
  • R. Çolak, Statistical convergence of order α, In: Modern Methods in Analysis and Its Applications (pp.121-129), Anamaya Publishers, New Delhi, (2010).
  • E. Gülle and U. Ulusu, Double Wijsman lacunary statistical convergence of order α, J. Appl. Math. Inform., 39(3-4) (2021), 303-319.
  • M. Mursaleen and O.H.H. Edely, Statistical convergence of double sequences, J. Math. Anal. Appl., 288(1) (2003), 223-231.
  • F. Nuray and B.E. Rhoades, Statistical convergence of sequences of sets, Fasc. Math., 49 (2012), 87-99.
  • F. Nuray, U. Ulusu and E. Dündar, Lacunary statistical convergence of double sequences of sets, Soft Comput., 20(7) (2016), 2883-2888.
  • F. Nuray and U. Ulusu, Lacunary invariant statistical convergence of double sequences of sets, Creat. Math. Inform., 28(2) (2019), 143-150.
  • F. Nuray, E. Dündar and U. Ulusu, Wijsman statistical convergence of double sequences of sets, Iran. J. Math. Sci. Inform., 16(1) (2021), 55-64.
  • N. Pancarog ̆lu and F. Nuray, On invariant statistically convergence and lacunary invariant statistical convergence of sequences of sets, Progress Appl. Math., 5(2) (2013), 23-29.
  • R.F. Patterson and E. Savaş, Lacunary statistical convergence of double sequences, Math. Commun., 10(1) (2005), 55-61.
  • A. Pringsheim, Zur theorie der zweifach unendlichen Zahlenfolgen, Math. Ann., 53(3) (1900), 289-321.
  • E. Savaş and R.F. Patterson, Double σ-convergence lacunary statistical sequences, J. Comput. Anal. Appl., 11(4) (2009), 610-615.
  • E. Savaş, Double almost statistical convergence of order α, Adv. Difference Equ., 2013(62) (2013), 9 pages.
  • E. Savaş, Double almost lacunary statistical convergence of order α, Adv. Difference Equ., 2013(254) (2013), 10 pages.
  • E. Savaş, On I-lacunary statistical convergence of order α for sequences of sets, Filomat, 29(6) (2015), 1223-1229.
  • H. Şengül and M. Et, On lacunary statistical convergence of order α, Acta Math. Sci. Ser. B, 34(2) (2014), 473-482.
  • H. Şengül and M. Et, On I-lacunary statistical convergence of order α of sequences of sets, Filomat, 31(8) (2017), 2403-2412.
  • U. Ulusu and F. Nuray, Lacunary statistical convergence of sequences of sets, Progress Appl. Math., 4(2) (2012), 99-109.
  • U. Ulusu and E. Gülle, Some statistical convergence types of order α for double set sequences, Facta Univ. Ser. Math. Inform., 35(3) (2020), 595-603.
There are 20 citations in total.

Details

Primary Language English
Journal Section Volume VII Issue I
Authors

Uğur Ulusu 0000-0001-7658-6114

Erdinç Dündar 0000-0002-0545-7486

Publication Date April 30, 2022
Published in Issue Year 2022 Volume: 7 Issue: 1

Cite

APA Ulusu, U., & Dündar, E. (2022). Invariant and Lacunary Invariant Statistical Convergence of Order $\eta$ for Double Set Sequences. Turkish Journal of Science, 7(1), 14-20.
AMA Ulusu U, Dündar E. Invariant and Lacunary Invariant Statistical Convergence of Order $\eta$ for Double Set Sequences. TJOS. April 2022;7(1):14-20.
Chicago Ulusu, Uğur, and Erdinç Dündar. “Invariant and Lacunary Invariant Statistical Convergence of Order $\eta$ for Double Set Sequences”. Turkish Journal of Science 7, no. 1 (April 2022): 14-20.
EndNote Ulusu U, Dündar E (April 1, 2022) Invariant and Lacunary Invariant Statistical Convergence of Order $\eta$ for Double Set Sequences. Turkish Journal of Science 7 1 14–20.
IEEE U. Ulusu and E. Dündar, “Invariant and Lacunary Invariant Statistical Convergence of Order $\eta$ for Double Set Sequences”, TJOS, vol. 7, no. 1, pp. 14–20, 2022.
ISNAD Ulusu, Uğur - Dündar, Erdinç. “Invariant and Lacunary Invariant Statistical Convergence of Order $\eta$ for Double Set Sequences”. Turkish Journal of Science 7/1 (April 2022), 14-20.
JAMA Ulusu U, Dündar E. Invariant and Lacunary Invariant Statistical Convergence of Order $\eta$ for Double Set Sequences. TJOS. 2022;7:14–20.
MLA Ulusu, Uğur and Erdinç Dündar. “Invariant and Lacunary Invariant Statistical Convergence of Order $\eta$ for Double Set Sequences”. Turkish Journal of Science, vol. 7, no. 1, 2022, pp. 14-20.
Vancouver Ulusu U, Dündar E. Invariant and Lacunary Invariant Statistical Convergence of Order $\eta$ for Double Set Sequences. TJOS. 2022;7(1):14-20.