Journal of Applied and Pure Mathematics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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AN APPLICATION OF MARKOV'S EXTENDED INTERVAL ARITHMETIC TO INTERVAL-VALUED SEQUENCE SPACES: A SPECIAL EXAMPLE

  • Received : 2023.09.27
  • Accepted : 2024.06.07
  • Published : 2024.07.30
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Abstract

In the classical sense, it is known that it is impossible to construct a vector space over the entire set of real numbers with the help of simple interval arithmetic. In this article, it has shown that a vector space can be constructed in the classical sense by helping Markov's extended interval arithmetic on the interval valued Cesaro sequence spaces of non-absolute type. As a result of the positive answers, this idea was extended by us with some theorems. Consequently, a new perspective was gained to the construction of new types of sequence spaces by using different algebraic operations on interval-valued sequence spaces.

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References

  1. B. Altay, F. Basar, Certain topological properties and duals of the matrix domain of a triangle matrix in a sequence space, J. Math. Anal. Appl. 336 (2007), 632-645. https://doi.org/10.1016/j.jmaa.2007.03.007
  2. F. Basar, Summability Theory and its Applications, ISBN:978-1-60805-420-6, Bentham e-books.
  3. F. Basar, Matrix transformations between certain sequence spaces of Xp and ℓp, Soochow J. Math. 26 (2000), 191-204
  4. F. Basar, R.C olak, Almost-conservative matrix transformations, Turk. J. Math. 13 (1989), 91-100.
  5. K.-P. Chiao, Fundamental properties of interval vector max-norm, Tamsui Oxford Journal of Mathematical Sciences 18 (2002), 219-233.
  6. P.S. Dwyer, Linear Computation, New York, Wiley, 1951.
  7. P.S. Dwyer, Erros of Matrix Computation, Simultaneous Equations and Eigenvalues, National Bureu of Standarts, Applied Mathematics Series 29 (1953), 49-58.
  8. P.S. Fischer, Automatic Propagated and Round-off Error Analysis, paper presented at the 13th national meeting of the Association for Computing Machinary, June 1958.
  9. B. Kuttner, On dual summability methods, Proc. Comb. Phil. Soc. 71 (1972), 67-73. https://doi.org/10.1017/S0305004100050283
  10. E. Kreyzing, Introduction Functional Analysis with Applications, Jhon Wiley and Sons. Inc., Canada, 1978.
  11. G.G. Lorentz, K.Zeller, Summation of sequences and summation of series, Proc. Camb. Phil. Soc. 71 (1972), 67-73. https://doi.org/10.1017/S0305004100050283
  12. S.M. Markov, Extended Interval Arithmetic Involving Infinite Intervals, Mathematica Balkanica, New Series 6 (1992), Fasc.3.
  13. R.E. Moore, Automatic Error Analysis in Digital Computation, LSMD-48421, Lockheed Missiles and Space Company, 1959.
  14. R.E. Moore and C.T. Yang, Theory of an Interval Algebra and Its Application to Numeric Analysis, RAAG Memoris II, Gaukutsu Bunken Fukeyu-kai, Tokyo, 1958.
  15. R.E. Moore and C.T. Yang, Interval Analysis I, LMSD-285875, Lockheed Missiles and Space Company, Palo Alto, Calif., 1959.
  16. Ng Peng-Nung and Lee Peng-Yee, Cesaro sequence spaces of non-absolute type, Annales Societatis Mathematicae Polonae Series I: Commentationes Mathematicae Xx (1978) Roczniki Polskiego Towarzystwa Matematycznego Seria I: Prace Matematyczne X X, 1978.
  17. M. Sengonul, A. Eryilmaz, On the Sequence Spaces of Interval Numbers, Thai Journal of Mathematics 8 (2010).
  18. M. Sengonul, On the Zweier sequence space, Demonstratio Mathematica 40 (2007).
  19. L.P. Yee, Cesaro sequence spaces, Math. Chronicle 1 (1984), 29-45.