Research Article
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Year 2022, Volume: 10 Issue: 2, 93 - 101, 01.06.2022
https://doi.org/10.36753/mathenot.692053
https://izlik.org/JA22ZN84XW

Abstract

References

  • [1] Chiao, K.-P.: Fundamental properties of interval vector max-norm. Tamsui Oxf. J. Math. Sci. 18 (2), 219-233 (2002).
  • [2] Dwyer, P. S.: Linear Computations. Wiley, New York (1951).
  • [3] Dwyer, P. S.: Errors of matrix computation, simultaneous equations and eigenvalues, National Bureu of Standarts. Applied Mathematics Series. 29, 49-58 (1953).
  • [4] Fast, H.: Sur la convergence statistique. Colloq. Math. 2, 241-244 (1951).
  • [5] Fridy, J. A.: On statistical convergence. Analysis (Munich). 5 (4), 301-314 (1985).
  • [6] Gürdal, M., Huban, M. B.: On I-convergence of double sequences in the Topology induced by random 2-norms. Matematicki Vesnik. 66 (1), 73-83 (2014).
  • [7] Gürdal, M., S ̧ahiner, A.: Extremal I-limit points of double sequences. Appl. Math. E-Notes. 8, 131-137 (2008).
  • [8] Markov,S.M.:Extendedintervalarithmeticinvolvinginfiniteintervals.Math.Balkanica,NewSeries.6(3),269-304 (1992).
  • [9] Markov, S.: On directed interval arithmetic and its applications. J.UCS. 1 (7), 514-526 (1995).
  • [10] Markov,S.:Quasilinearspacesandtheirrelationtovectorspaces.ElectronicJournalonMathematicsofComputation. 2 (1), 1-21 (2005).
  • [11] Moore,R.E.:Automaticerroranalysisindigitalcomputation.LockheedMissilesandSpaceCompany,Technical Report LMSD-448421. California (1959).
  • [12] Moore, R. E., Yang, C. T.: Interval analysis I. Lockheed Missiles and Space Division, Technical Report LMSD- 288139. California (1960).
  • [13] Schoenberg, I. J.: The integrability of certain functions and related summability methods. Amer. Math. Monthly. 66 (5), 361-375 (1959).
  • [14] Sunaga, T.: Theory of an interval algebra and its application to numerical analysis. In: Research Association of Applied Geometry Memoirs II (pp. 29-46). Gakujutsu Bunken Fukyu-kai, Tokyo (1958).
  • [15] S ̧engönül, M., Eryilmaz, A.: On the sequence spaces of interval numbers. Thai J. Math. 8 (3), 503-510 (2010).

Some Properties of Two Dimensional Interval Numbers

Year 2022, Volume: 10 Issue: 2, 93 - 101, 01.06.2022
https://doi.org/10.36753/mathenot.692053
https://izlik.org/JA22ZN84XW

Abstract

In this paper, we will introduce the notion of convergence of two dimensional interval sequences and show that the set of all two dimensional interval numbers is a metric space. Also, some ordinary vector norms will be extended to the set of two dimensional interval vectors. Furthermore, we will give definitions of statistical convergence, statistically Cauchy and Cesaro summability for the two dimensional interval numbers and we will get the relationships between them.

References

  • [1] Chiao, K.-P.: Fundamental properties of interval vector max-norm. Tamsui Oxf. J. Math. Sci. 18 (2), 219-233 (2002).
  • [2] Dwyer, P. S.: Linear Computations. Wiley, New York (1951).
  • [3] Dwyer, P. S.: Errors of matrix computation, simultaneous equations and eigenvalues, National Bureu of Standarts. Applied Mathematics Series. 29, 49-58 (1953).
  • [4] Fast, H.: Sur la convergence statistique. Colloq. Math. 2, 241-244 (1951).
  • [5] Fridy, J. A.: On statistical convergence. Analysis (Munich). 5 (4), 301-314 (1985).
  • [6] Gürdal, M., Huban, M. B.: On I-convergence of double sequences in the Topology induced by random 2-norms. Matematicki Vesnik. 66 (1), 73-83 (2014).
  • [7] Gürdal, M., S ̧ahiner, A.: Extremal I-limit points of double sequences. Appl. Math. E-Notes. 8, 131-137 (2008).
  • [8] Markov,S.M.:Extendedintervalarithmeticinvolvinginfiniteintervals.Math.Balkanica,NewSeries.6(3),269-304 (1992).
  • [9] Markov, S.: On directed interval arithmetic and its applications. J.UCS. 1 (7), 514-526 (1995).
  • [10] Markov,S.:Quasilinearspacesandtheirrelationtovectorspaces.ElectronicJournalonMathematicsofComputation. 2 (1), 1-21 (2005).
  • [11] Moore,R.E.:Automaticerroranalysisindigitalcomputation.LockheedMissilesandSpaceCompany,Technical Report LMSD-448421. California (1959).
  • [12] Moore, R. E., Yang, C. T.: Interval analysis I. Lockheed Missiles and Space Division, Technical Report LMSD- 288139. California (1960).
  • [13] Schoenberg, I. J.: The integrability of certain functions and related summability methods. Amer. Math. Monthly. 66 (5), 361-375 (1959).
  • [14] Sunaga, T.: Theory of an interval algebra and its application to numerical analysis. In: Research Association of Applied Geometry Memoirs II (pp. 29-46). Gakujutsu Bunken Fukyu-kai, Tokyo (1958).
  • [15] S ̧engönül, M., Eryilmaz, A.: On the sequence spaces of interval numbers. Thai J. Math. 8 (3), 503-510 (2010).
There are 15 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Research Article
Authors

Fatih Nuray 0000-0003-0160-4001

Uğur Ulusu 0000-0001-7658-6114

Erdinç Dundar 0000-0002-0545-7486

Submission Date February 20, 2020
Acceptance Date January 14, 2021
Publication Date June 1, 2022
DOI https://doi.org/10.36753/mathenot.692053
IZ https://izlik.org/JA22ZN84XW
Published in Issue Year 2022 Volume: 10 Issue: 2

Cite

APA Nuray, F., Ulusu, U., & Dundar, E. (2022). Some Properties of Two Dimensional Interval Numbers. Mathematical Sciences and Applications E-Notes, 10(2), 93-101. https://doi.org/10.36753/mathenot.692053
AMA 1.Nuray F, Ulusu U, Dundar E. Some Properties of Two Dimensional Interval Numbers. Math. Sci. Appl. E-Notes. 2022;10(2):93-101. doi:10.36753/mathenot.692053
Chicago Nuray, Fatih, Uğur Ulusu, and Erdinç Dundar. 2022. “Some Properties of Two Dimensional Interval Numbers”. Mathematical Sciences and Applications E-Notes 10 (2): 93-101. https://doi.org/10.36753/mathenot.692053.
EndNote Nuray F, Ulusu U, Dundar E (June 1, 2022) Some Properties of Two Dimensional Interval Numbers. Mathematical Sciences and Applications E-Notes 10 2 93–101.
IEEE [1]F. Nuray, U. Ulusu, and E. Dundar, “Some Properties of Two Dimensional Interval Numbers”, Math. Sci. Appl. E-Notes, vol. 10, no. 2, pp. 93–101, June 2022, doi: 10.36753/mathenot.692053.
ISNAD Nuray, Fatih - Ulusu, Uğur - Dundar, Erdinç. “Some Properties of Two Dimensional Interval Numbers”. Mathematical Sciences and Applications E-Notes 10/2 (June 1, 2022): 93-101. https://doi.org/10.36753/mathenot.692053.
JAMA 1.Nuray F, Ulusu U, Dundar E. Some Properties of Two Dimensional Interval Numbers. Math. Sci. Appl. E-Notes. 2022;10:93–101.
MLA Nuray, Fatih, et al. “Some Properties of Two Dimensional Interval Numbers”. Mathematical Sciences and Applications E-Notes, vol. 10, no. 2, June 2022, pp. 93-101, doi:10.36753/mathenot.692053.
Vancouver 1.Fatih Nuray, Uğur Ulusu, Erdinç Dundar. Some Properties of Two Dimensional Interval Numbers. Math. Sci. Appl. E-Notes. 2022 Jun. 1;10(2):93-101. doi:10.36753/mathenot.692053

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