Matrix transformation on statistically convergent sequence spaces of interval number sequences
DOI:
https://doi.org/10.4067/S0716-09172016000200004Keywords:
Interval number, sequence space, statistical convergence, matrix transformations, intervalos, espacio secuencial, convergencia estadística, transformaciones de matriz.Abstract
The main purpose of this paper is to introduce the necessary and sufficient conditions for the matrix of interval numbers Ā = (ānk) such that Ā-transform of x = (xk) belongs to the sets c0S(i) ∩ ℓi∞, cS(i) ∩ ℓi∞, where in particular x ∈ c0S(i) ∩ ℓi∞ and x ∈ cS(i) ∩ ℓi∞ respectively.References
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[3] A. Esi, Lacunary sequence spaces of interval numbers, Thai J. Math., 10(2): pp. 445-451, (2012).
[4] A. Esi, A-Sequence spaces of interval numbers, Appl. Math. and Inform. Sci., 8(3): pp. 1099-1102, (2014).
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[7] A. Esi and N. Braha, On asymptotically -statistical equivalent sequences of interval numbers,Acta Scientarium. Techno., 35(3): pp.
515-520, (2013).
[8] A. Esi and A. Esi, Asymptotically lacunary statistically equivalent sequences of interval numbers ,Int. J. Math. Appl., 1(1): pp. 43-48,
(2013).
[9] A. Esi and B. Hazarika, Some ideal convergence of double-interval number sequences defined by Orlicz function, Global J. Math. Anal.,1(3): pp. 110-116, (2013).
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[11] B.C. Tripathy, Matrix transformation between some classes of sequences, J. Math. Anal. Appl., 206: pp. 448-450, (1997).
[12] B.C. Tripathy, Matrix transformation between series and sequences, Bull. Malaysian Math. Soc. (Second series), 21: pp. 17—20, (1998).
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(1995)
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[19] I. J. Schoenberg, The integrability of certain functions and related summability methods, Am. Math. Mon., 66(5): pp. 361-375, (1959).
[20] J. A. Fridy, On statistical convergence,Analysis, 5(4): pp. 301-313, (1985).
[21] Kuo-Ping Chiao, Fundamental properties of interval vector max-norm, Tamsui Oxford J. Math. Sci., 18(2): pp. 219-233, (2002).
[22] M. Sengönül and A.Eryilmaz, On the sequence spaces of interval numbers, Thai J. Math, 8(3): pp. 503-510, (2010).
[23] P. S. Dwyer, Linear Computation, New York, Wiley, (1951).
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[25] P. S. Fischer, Automatic propagated and round-off error analysis, Paper presented at the 13th national meeting of the Association for Computing Machinary, (1958).
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[27] R. E. Moore and C. T. Yang, Theory of an interval algebra and its application to numeric analysis, RAAG Memories II, Gaukutsu Bunken Fukeyu-kai, Tokyo, (1958).
[28] S. Debnath, A. J. Dutta and S. Saha, Regular matrix of interval numbers based on fibonacci numbers, Afr. Mat., 26(7): pp. 1379-1385, (2015)
[29] S. Debnath, B. Sarma and S. Saha, On some sequence spaces of interval vectors, Afr. Mat., 26(5): pp. 673-678, (2015).
[30] S. Debnath and S. Saha, On Statistically Convergent Sequence Spaces of Interval Numbers , Proceedings of IMBIC, 3: pp. 178-183, (2014).
[31] S. Nanda, Matrix transformations between sequence spaces, Queen’s papers in pure and Appl. Math., pp. 74, (1986).
[32] T. Salat, On statistical convergence sequences of real numbers, Math. Slovaca, 30: pp. 139-150, (1950).
[2] A. Esi, A new class of interval numbers, J. Qafqaz Univ. 31: pp. 98-102, (2011)
[3] A. Esi, Lacunary sequence spaces of interval numbers, Thai J. Math., 10(2): pp. 445-451, (2012).
[4] A. Esi, A-Sequence spaces of interval numbers, Appl. Math. and Inform. Sci., 8(3): pp. 1099-1102, (2014).
[5] A. Esi, Double lacunary sequence spaces of double sequence of interval numbers, Proyecciones, 31(1): pp. 297-306, (2012).
[6] A. Esi, Statistical and lacunary statistical convergence of interval numbers in topological groups, Acta Scientarium. Techno., 36(3): pp. 491-495, (2014).
[7] A. Esi and N. Braha, On asymptotically -statistical equivalent sequences of interval numbers,Acta Scientarium. Techno., 35(3): pp.
515-520, (2013).
[8] A. Esi and A. Esi, Asymptotically lacunary statistically equivalent sequences of interval numbers ,Int. J. Math. Appl., 1(1): pp. 43-48,
(2013).
[9] A. Esi and B. Hazarika, Some ideal convergence of double-interval number sequences defined by Orlicz function, Global J. Math. Anal.,1(3): pp. 110-116, (2013).
[10] A. Zygmund, Trigonometric Series, Cambridge University Press, Cambridge, UK. (1979).
[11] B.C. Tripathy, Matrix transformation between some classes of sequences, J. Math. Anal. Appl., 206: pp. 448-450, (1997).
[12] B.C. Tripathy, Matrix transformation between series and sequences, Bull. Malaysian Math. Soc. (Second series), 21: pp. 17—20, (1998).
[13] F. Basar, Summability theory and its applications, Bentham Science, (2011)
[14] H. Cakalli, A study on statistical convergence, Funct. Anal. Approx. Comput., 1(2): pp. 19-24, (2009).
[15] H. Fast, Sur la convergence statistique, Colloq. Math. 2: pp. 241-244, (1951).
[16] H. I. Miller, A measure theoretical subsequence characterization of statical convergence, Trans. Am. Math. Soc., 347(5): pp. 1811-1819,
(1995)
[17] H. Steinhus,Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math. 2: pp. 73-74, (1951).
[18] I.J. Maddox, On strong almost cconvergence, Math. Proc. Camb. Philos. Soc., 85(2): pp. 345-350, (1979).
[19] I. J. Schoenberg, The integrability of certain functions and related summability methods, Am. Math. Mon., 66(5): pp. 361-375, (1959).
[20] J. A. Fridy, On statistical convergence,Analysis, 5(4): pp. 301-313, (1985).
[21] Kuo-Ping Chiao, Fundamental properties of interval vector max-norm, Tamsui Oxford J. Math. Sci., 18(2): pp. 219-233, (2002).
[22] M. Sengönül and A.Eryilmaz, On the sequence spaces of interval numbers, Thai J. Math, 8(3): pp. 503-510, (2010).
[23] P. S. Dwyer, Linear Computation, New York, Wiley, (1951).
[24] P.S. Dwyer, Erros of matrix computation, simultaneous equations and eigenvalues, National Bureu of Standarts, Applied Mathematics Series, 29: pp. 49-58, (1953).
[25] P. S. Fischer, Automatic propagated and round-off error analysis, Paper presented at the 13th national meeting of the Association for Computing Machinary, (1958).
[26] R. E. Moore, Automatic error analysis in digital computation, LSMD-48421,Lockheed Missiles and Space Company, (1959).
[27] R. E. Moore and C. T. Yang, Theory of an interval algebra and its application to numeric analysis, RAAG Memories II, Gaukutsu Bunken Fukeyu-kai, Tokyo, (1958).
[28] S. Debnath, A. J. Dutta and S. Saha, Regular matrix of interval numbers based on fibonacci numbers, Afr. Mat., 26(7): pp. 1379-1385, (2015)
[29] S. Debnath, B. Sarma and S. Saha, On some sequence spaces of interval vectors, Afr. Mat., 26(5): pp. 673-678, (2015).
[30] S. Debnath and S. Saha, On Statistically Convergent Sequence Spaces of Interval Numbers , Proceedings of IMBIC, 3: pp. 178-183, (2014).
[31] S. Nanda, Matrix transformations between sequence spaces, Queen’s papers in pure and Appl. Math., pp. 74, (1986).
[32] T. Salat, On statistical convergence sequences of real numbers, Math. Slovaca, 30: pp. 139-150, (1950).
Published
2017-03-23
How to Cite
[1]
S. Debnath and S. Saha, “Matrix transformation on statistically convergent sequence spaces of interval number sequences”, Proyecciones (Antofagasta, On line), vol. 35, no. 2, pp. 187-195, Mar. 2017.
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