Some Properties of Two Dimensional Interval Numbers

Year 2022, Volume: 10 Issue: 2, 93 - 101, 01.06.2022

Fatih Nuray Uğur Ulusu Erdinç Dundar

https://doi.org/10.36753/mathenot.692053

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.

Keywords

convergent sequence, metric spaces, interval number sequence, two dimensional interval number

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).