Some new sequence spaces of interval number based on Zweier sequences and Fibonacci numbers

  • Shyamal Debnath Tripura University
  • Ayhan Esi Adiyaman University
  • Subrata Saha Tripura University
Keywords: Matrix transformations, interval number, Zweier sequence, Fibonacci number

Abstract

The main aim of this paper is to determine necessary and sufficient conditions for the matrix of interval numbers $\bar{A}=(\bar{a}_{nk})$ such that $\bar{A}$ transform $\bar{x}=(\bar{x}_{k})$, belongs to the set $l_{\infty }^{i}$, $c_{0}^{i}$, $c^{i}$ where in particular $\bar{x}\in l_{\infty }^{i}$, $c_{0}^{i}$ and $c^{i} $, to introduce some new sequence spaces $c^{i}(\bar{A}_{ZF})$, $c_{0}^{i}(\bar{A}_{ZF})$, $l_{\infty }^{i}(\bar{A}_{ZF})$ based on a
newly defined matrix of interval numbers $\bar{A}_{ZF}$. We study some basic algebraic and topological properties. Also we investigate the relations related to these spaces.

References

Altay, B.; Basar, F. and Mursaleen, M. On the Euler sequence space which include the space $l_{p}$ and $l_{infty}$. Inform Sci., 176 (10) (2006), 1450--1462.

Basar, F. and Altay, B. On the spaces of sequences of p-bounded variation and related matrix mappings. Ukrainian Math. J. 55(1) (2003), 136-144.

Basar, F. Summability Theory and its applications. 2011.

Chiao, K. P. Fundamental Properties of Interval Vector max-norm. Tamsui Oxford J. Math. Sci., 18(2) (2002), 219-233.

Debnath, S. and Saha, S. Matrix Transformation on Statistically Convergent Sequence Spaces of Interval Number Sequences. Proecciones J. Mathematics, 35(1) (2016), 187-195.

Debnath, S. and Saha, S. On Statistically Convergent Sequence Spaces of Interval Numbers, Proceedings of IMBIC, 3 (2014), 178-183.

Debnath, S. and Saha, S. Some Newly Defined Sequence Spaces Using Regular Matrix of Fibonacci Numbers. AKU J. Sci. Engi, 14 (2014), 011301, 1-3.

Debnath, S.; Datta, A. J. and Saha, S. Regular Matrix of Interval Numbers based on Fibonacci Numbers. Afrika Mathematika, 26(7) (2015), 1379-1385.

Debnath, S.; Sarma, B. and Saha, S. On Some Sequence Spaces of Interval vectors. Afrika Mathematika, 26(5) (2015), 673-678.

Dwyer, P. S. Linear Computation. New York, Wiley, 1951.

Dwyer, P. S. Erros of Matrix Computation, Simultaneous Equations and Eigenvalues. National Bureu of Standarts, Applied Mathematics Series, 29 (1953), 49-58.

Esi, A. A new class of double interval numbers. Sci. Magna, 7(4) (2013), 54-59.

Esi, A. A new class of interval numbers. J. Qafqaz Univ., 31 (2011), 98-102.

Esi, A. and Acikgoz, M. On some double lacunary strong Zweier convergent sequence spaces. Annals Univ. Craiova, Math. Comp. Sci. Series, 40(2) (2013), 121-127.

Esi, A. and Sapsizoglu, A. On some lacunary σ-strong Zweier convergent sequence spaces. Romai J., 8(2) (2013), 61-70.

Esi, A. Double lacunary sequence spaces of double sequence of interval numbers. Proyecciones J. Math, 31(1) (2012), 297-306.

Esi, A. Lacunary Sequence Spaces of Interval Numbers. Thai J. Math, 10(2) (2012), 445-451.

Esi, A. λ-Sequence spaces of interval numbers. Appl. Math. Inform. Sci, 8(3) (2014), 1099-1102.

Esi, A. Statistical and lacunary statistical convergence of interval numbers in topological groups. Acta Scien. Tech., 36(3) (2014), 491-495.

Esi, A. Strongly almost λ-convergence and statistically almost λ-convergence of interval numbers. Sci. Magna, 7(2) (2011), 117-122.

Esi, Ayhan and Esi, Ayten. Asymptotically lacunary statistically equivalent sequences of interval numbers. Int. J. Math. Appl., 1(1) (2013), 43-48.

Fischer, P. S. Automatic Propagated and Round-off Error Analysis. paper presented at the 13th national meeting of the Association for Computing Machinary, 1958.

Karababa, Y. F. and Esi, A. On some strong zweier convergent sequence spaces. Acta Univ. Apulensis, 29 (2013), 9-15.

Malkowsky, E. Recent results in the theory of matrix transformation in sequence spaces. Math. Vensik, 49 (1997) 187-196.

Moore, R. E. and Yang, C. T. Theory of an Interval Algebra and Its Application to Numeric Analysis, RAAG Memories II, Gaukutsu Bunken Fukeyu-kai, Tokyo, 1958.

Moore, R. E. Automatic Error Analysis in Digital Computation. LSMD-48421, Lockheed Missiles and Space Company, 1959.

Savas, E. and Mursaleen, M. Matrix transformations in some sequence spaces. Istanbul Universitesi Fen Fak. Mat. Dergisi, 52 (1993), 1-5.

Sengonul, M. and Eryilmaz, A. On the Sequence Spaces of Interval Numbers. Thai J. Math, 8(3) (2010), 503-510.

Sengonul, M. On the Zweier sequence space. Demons. Mathematica, XL(1) (2007), 181-196.

Tripathy, B. C. Matrix transformation between series and sequences. Bull. Malaysian Math. Soc. (second Series), 21 (1998), 17-20.

Tripathy, B. C. Matrix transformation between some classes of sequences. J. Math. Anal. Appl., 206 (1997), 448-450.

Published
2018-06-29
How to Cite
Debnath, S., Esi, A., & Saha, S. (2018). Some new sequence spaces of interval number based on Zweier sequences and Fibonacci numbers. Divulgaciones Matemáticas, 19(2), 36-43. Retrieved from https://produccioncientificaluz.org/index.php/divulgaciones/article/view/36610