On some spaces of Lacunary I-convergent sequences of interval numbers defined by sequence of moduli
DOI:
https://doi.org/10.4067/S0716-09172017000200325Keywords:
Interval numbers, Ideal, Filter, , I-convergent sequence, Solid and monotone space, Banach space, Modulus functionAbstract
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References
[1] ESI, A. (2012) A new class of interval numbers. EN: Journal of Qafqaz University, Mathematics and Computer Science. [s.l.: s.n.], 98-102.
[2] ESI, A. (2012) Lacunary sequence spaces of interval numbers. EN: Thai Journal of Mathemaatics, 10 (2). [s.l.: s.n.], 445-451.
[3] ESI, A. (2012) Double lacunary sequence spaces of double Sequence of interval numbers. EN: Proyecciones Journal of Mathematics, 31 (1). [s.l.: s.n.], 297-306.
[4 ESI, A. (2011) Strongly almost -convergence and statistically almost -convergence of interval numbers. EN: Scientia Magna, 7 (2). [s.l.: s.n.], 117-122.
[5] ESI, A. (2014) Statistical and lacunary statistical convergence of interval numbers in topological groups. EN: Acta Scientarium Technology. [s.l.: s.n.].
[6] ESI, A. (2013) On asymptotically -statistical equivalent sequences of interval numbers. EN: Acta Scientarium Technology, 35 (3). [s.l.: s.n.], 515-520
[7] ESI, A. (2013) Asymptotically lacunary statistically equivalent sequences of interval numbers, International Journal of Mathematics and Its Applications, 1(1). [s.l.: s.n.], 43-48.
[8] ESI, A. (2013) Some I-convergent of double ?-interval sequences defined by Orlicz function., Global, J. of Mathematical Analysis, 1 (3). [s.l.: s.n.], 110-116.
[9] ESI, A. (2014) ?-Sequence Spaces of Interval Numbers. EN: Appl. Math. Inf. Sci. 8(3). [s.l.: s.n.], 1099-1102.
[10] BUCK, R. C. (1953) Generalized asymptotic density,Amer. EN: J. Math. 75. [s.l.: s.n.], 335-346.
[11] CHIAO, K. P. (2002) Fundamental properties of interval vector max-norm. EN: Tamsui Oxford Journal of Mathematical Sciences, 18(2). [s.l.: s.n.], 219-233.
[12] DWYER, P. S. (1951) Linear Computation. New York: Wiley.
[13] FAST, H. (1951) Sur la convergence statistique. EN: Colloq. Math. 2. [s.l.: s.n.], 241-244.
[14] FREEDMAN, A. R.(1978) Sember,J.J.and Raphael,M.,Some Cesaro type summability spaces. EN: Proc. London Math. Soc., 37. [s.l.: s.n.], 508-520.
[15] FRIDY, J. A. (1985) On statistical convergence. EN: Analysis, 5. [s.l.: s.n.], 301-313.
[16] KHAN, V. A. (2014) Mohd Shafiq and Ebadullah, K., On paranorm Iconvergent sequence spaces of interval numbers. EN: J. of Nonlinear Analysis and Optimisation (Theory and Application), 5(1). [s.l.: s.n.], 103-114.
[17] ] KHAN, V. A. (2014) On paranorm BV? Iconvergent sequence spaces defined by an Orlicz function. EN: Global Journal of mathematical Analysis, 2 (2). [s.l.: s.n.], 28-43.
[18] KOLK, E. (1993) On strong boundedness and summability with respect to a sequence of moduli. EN: Acta Comment.Univ.Tartu., 960. [s.l.: s.n.], 41-50.
[19] KOLK, E. (1994) Inclusion theorems for some sequence spaces defined by a sequence of moduli. EN: Acta Comment.Univ. Tartu., 970. [s.l.: s.n.], 65-72.
[20] KOSTYRKO, P. (20??) Statistical convergence and Iconvergence.Real Analysis Exchange.
[21] KOSTYRKO, P. (2000) I-convergence,Raal Analysis. EN: Analysis Exchange. 26(2). [s.l.: s.n.], 669-686.
[22] MOORE, R. E. (1959) Automatic Error Analysis in Digital Computation, LSMD-48421, Lockheed Missiles and Space Company. [s.l.: s.n.].
[23] MOORE, R. E. (1959) Interval Analysis I, LMSD-285875, Lockheed Missiles and Space Company, Palo Alto, Calif. [s.l.: s.n.].
[24] MURSALEEN, M. (2010) On the Spaces of ?-Convergent and Bounded Sequences. EN: Thai Journal of Mathematics 8(2). [s.l.: s.n.], 311-329.
[25] MURSALEEN, M. (2014) Spaces of Ideal Convergent sequences. Article ID 134534, 6 pages. [s.l.: s.n.]. http://dx.doiorg/10.1155/2014/134534.
[26] NAKANO, H. (1953) Concave modulars. EN: J. Math Soc. Japan, 5. [s.l.: s.n.], 29-49.
[27] RUCKLE, W. H. (1968) On perfect Symmetric BK-spaces. EN: Math. Ann. 175. [s.l.: s.n.], 121-126.
[28] RUCKLE, W. H. (1967) Symmetric coordinate spaces and symmetric bases. EN: Canad. J. Math. 19. [s.l.: s.n.], 828-838.
[29] RUCKLE, W. H. (1973) FK-spaces in which the sequence of coordinate vectors is bounded. EN: Canad. J. Math. 25 (5). [s.l.: s.n.], 973-975.
[30] SALÁT, T. (1980) On statistical convergent sequences of real numbers. En: Math, Slovaca 30. [s.l.: s.n.].
[31] SALÁT, T. (2004) On some properties of Iconvergence Tatra Mt. EN: Math. Publ. 28. [s.l.: s.n.], 279-286.
[32] SALÁT, T. (2005) On I-convergence field. EN: Ital. J. Pure Appl. Math. 17. [s.l.: s.n.], 45-54.
[33] SCHOENBERG, I. J. (1959) The integrability of certain functions and related summability methods. EN: Amer. Math. Monthly, 66. [s.l.: s.n.], 361-375.
[34] SENGÖNÜL, M. (2010) On the Sequence Spaces of Interval Numbers. EN: Thai J. of Mathematics, 8(3). [s.l.: s.n.], 503-510.
[35] TRIPATHY, B. C. (1998) On statistical convergence. EN: Proc. Estonian Acad. Sci. Phy. Math. Analysis. [s.l.: s.n.], 299-303.
[36] TRIPATHY, B. C. (2009) Paranorm I-convergent sequence spaces. EN: Math. Slovaca 59 (4). [s.l.: s.n.], 485-494.
[2] ESI, A. (2012) Lacunary sequence spaces of interval numbers. EN: Thai Journal of Mathemaatics, 10 (2). [s.l.: s.n.], 445-451.
[3] ESI, A. (2012) Double lacunary sequence spaces of double Sequence of interval numbers. EN: Proyecciones Journal of Mathematics, 31 (1). [s.l.: s.n.], 297-306.
[4 ESI, A. (2011) Strongly almost -convergence and statistically almost -convergence of interval numbers. EN: Scientia Magna, 7 (2). [s.l.: s.n.], 117-122.
[5] ESI, A. (2014) Statistical and lacunary statistical convergence of interval numbers in topological groups. EN: Acta Scientarium Technology. [s.l.: s.n.].
[6] ESI, A. (2013) On asymptotically -statistical equivalent sequences of interval numbers. EN: Acta Scientarium Technology, 35 (3). [s.l.: s.n.], 515-520
[7] ESI, A. (2013) Asymptotically lacunary statistically equivalent sequences of interval numbers, International Journal of Mathematics and Its Applications, 1(1). [s.l.: s.n.], 43-48.
[8] ESI, A. (2013) Some I-convergent of double ?-interval sequences defined by Orlicz function., Global, J. of Mathematical Analysis, 1 (3). [s.l.: s.n.], 110-116.
[9] ESI, A. (2014) ?-Sequence Spaces of Interval Numbers. EN: Appl. Math. Inf. Sci. 8(3). [s.l.: s.n.], 1099-1102.
[10] BUCK, R. C. (1953) Generalized asymptotic density,Amer. EN: J. Math. 75. [s.l.: s.n.], 335-346.
[11] CHIAO, K. P. (2002) Fundamental properties of interval vector max-norm. EN: Tamsui Oxford Journal of Mathematical Sciences, 18(2). [s.l.: s.n.], 219-233.
[12] DWYER, P. S. (1951) Linear Computation. New York: Wiley.
[13] FAST, H. (1951) Sur la convergence statistique. EN: Colloq. Math. 2. [s.l.: s.n.], 241-244.
[14] FREEDMAN, A. R.(1978) Sember,J.J.and Raphael,M.,Some Cesaro type summability spaces. EN: Proc. London Math. Soc., 37. [s.l.: s.n.], 508-520.
[15] FRIDY, J. A. (1985) On statistical convergence. EN: Analysis, 5. [s.l.: s.n.], 301-313.
[16] KHAN, V. A. (2014) Mohd Shafiq and Ebadullah, K., On paranorm Iconvergent sequence spaces of interval numbers. EN: J. of Nonlinear Analysis and Optimisation (Theory and Application), 5(1). [s.l.: s.n.], 103-114.
[17] ] KHAN, V. A. (2014) On paranorm BV? Iconvergent sequence spaces defined by an Orlicz function. EN: Global Journal of mathematical Analysis, 2 (2). [s.l.: s.n.], 28-43.
[18] KOLK, E. (1993) On strong boundedness and summability with respect to a sequence of moduli. EN: Acta Comment.Univ.Tartu., 960. [s.l.: s.n.], 41-50.
[19] KOLK, E. (1994) Inclusion theorems for some sequence spaces defined by a sequence of moduli. EN: Acta Comment.Univ. Tartu., 970. [s.l.: s.n.], 65-72.
[20] KOSTYRKO, P. (20??) Statistical convergence and Iconvergence.Real Analysis Exchange.
[21] KOSTYRKO, P. (2000) I-convergence,Raal Analysis. EN: Analysis Exchange. 26(2). [s.l.: s.n.], 669-686.
[22] MOORE, R. E. (1959) Automatic Error Analysis in Digital Computation, LSMD-48421, Lockheed Missiles and Space Company. [s.l.: s.n.].
[23] MOORE, R. E. (1959) Interval Analysis I, LMSD-285875, Lockheed Missiles and Space Company, Palo Alto, Calif. [s.l.: s.n.].
[24] MURSALEEN, M. (2010) On the Spaces of ?-Convergent and Bounded Sequences. EN: Thai Journal of Mathematics 8(2). [s.l.: s.n.], 311-329.
[25] MURSALEEN, M. (2014) Spaces of Ideal Convergent sequences. Article ID 134534, 6 pages. [s.l.: s.n.]. http://dx.doiorg/10.1155/2014/134534.
[26] NAKANO, H. (1953) Concave modulars. EN: J. Math Soc. Japan, 5. [s.l.: s.n.], 29-49.
[27] RUCKLE, W. H. (1968) On perfect Symmetric BK-spaces. EN: Math. Ann. 175. [s.l.: s.n.], 121-126.
[28] RUCKLE, W. H. (1967) Symmetric coordinate spaces and symmetric bases. EN: Canad. J. Math. 19. [s.l.: s.n.], 828-838.
[29] RUCKLE, W. H. (1973) FK-spaces in which the sequence of coordinate vectors is bounded. EN: Canad. J. Math. 25 (5). [s.l.: s.n.], 973-975.
[30] SALÁT, T. (1980) On statistical convergent sequences of real numbers. En: Math, Slovaca 30. [s.l.: s.n.].
[31] SALÁT, T. (2004) On some properties of Iconvergence Tatra Mt. EN: Math. Publ. 28. [s.l.: s.n.], 279-286.
[32] SALÁT, T. (2005) On I-convergence field. EN: Ital. J. Pure Appl. Math. 17. [s.l.: s.n.], 45-54.
[33] SCHOENBERG, I. J. (1959) The integrability of certain functions and related summability methods. EN: Amer. Math. Monthly, 66. [s.l.: s.n.], 361-375.
[34] SENGÖNÜL, M. (2010) On the Sequence Spaces of Interval Numbers. EN: Thai J. of Mathematics, 8(3). [s.l.: s.n.], 503-510.
[35] TRIPATHY, B. C. (1998) On statistical convergence. EN: Proc. Estonian Acad. Sci. Phy. Math. Analysis. [s.l.: s.n.], 299-303.
[36] TRIPATHY, B. C. (2009) Paranorm I-convergent sequence spaces. EN: Math. Slovaca 59 (4). [s.l.: s.n.], 485-494.
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2017-06-02
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How to Cite
[1]
“On some spaces of Lacunary I-convergent sequences of interval numbers defined by sequence of moduli”, Proyecciones (Antofagasta, On line), vol. 36, no. 2, pp. 325–346, Jun. 2017, doi: 10.4067/S0716-09172017000200325.