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On some generalised I-convergent sequence spaces of double interval numbers

Year 2016, Volume: 4 Issue: 2, 125 - 137, 01.03.2016

Vakeel A. Khan Ayhan Esi Yasmeen Yasmeen Hira Fatima

Abstract

In this article we introduce and study some spaces of I-convergent sequences of double interval numbers with the help of a  double sequence F = ( fi, j) of modulii and double bounded sequence p = (pi, j) of positive real numbers. We study some topological  and algebraic properties, prove the decomposition theorem and study some inclusion relations on these spaces.


Keywords

Double interval numbers ideal filter double I-convergent sequence spaces solid and monotone space Banach space

References

  • E. Ayhan and B. Hazarika, Some I-convergent of duoble ∧-interval number sequences defined by Orlicz function, Global, J. of Mathmatical Analysis,1,No. 3,110-116 (2013).
  • E. Ayhan, -sequence spces of interval numbers, Appl.Math. Inf., 8, No. 3, 1099-1102 (2014).
  • R. C. Buck, Generalized asymptotic density, Amer., J. Math.,75 , 335-346 (1953).
  • K. P. Chiao, Fundamental properties of interval vector max-norm, Tamsui Oxford Journal of Mathematical Science, 18, No. 2, 219-233 (2002).
  • P. S. Dwyer, Linear computation, New York, Wiley, (1951).
  • H. Fast, Sur la convergence statistique, Colloq. Math.,2, 241-244 (1951).
  • J. A. Fridy, On statistical convergence, Analysis, 5, 301-313 (1985).
  • V. A. Khan, mohd. Shafiq and K. Ebadullah, On paranorm I-convergent sequence spaces of interval numbers, J. of Nonlinear analysis and Optimisation (Theory and Application), 5, No. 1, 103-114 (2014).
  • V. K. Khan, Ahyan Esi. and Mohd. Shafiq, On paranorm BVI-convergent sequence spaces defined by an Orlicz function, Global Journal of Mathematical Analysis, 2, No. 2, 28-43 (2014).
  • V. A. Khan and Mohd. Shafiq, On some generalized I-convergent sequence spaces of interval numbers, 10, No. 3,00-00 (2014).
  • V. A. Khan, Suthep Suantai and K. Ebadullah, On some I-convergent sequence spaces defined by a sequence of modulii, J. of Nonlinear analysis and Optimisation, 3, No. 2, 145-152 (2012).
  • E. Kolk, On strong boundedness and summability with respect to a sequence of moduli, Acta Comment. Univ. Tartu., 960, 41-50 (1993).
  • E. Kolk, Inclusion theorems for some sequence spaces defined by a sequence of moduli, Acta Comment. Univ. Tartu., 970 65-72 (1994).
  • P. Kostyrko, M. Macaj and T. Salat, Statistical convergence and I- convergence, Real Analysis Exchange.
  • P. Kostyrko, T. Salat and W. Wilczynski, I-convergence, Real Analysis Exchange 26, No. 2, 669-686 (2000).
  • R. E. Moore, Automatic error analysis in digital computation, LSMD-48421, Lockheed Missiles and Space Company, (1959). R. E.Moore and C. T. Yang, Interval Analysis I, LMSD-285875, Lockheed Missiles and Space Company, Palo Alto, Calif., (1959).
  • M. Mursaleen and K. Noman Abdullah, On the spaces of -convergent and bounded sequences, Thai Journal of Mathematics, 8, No. 2, 311-329 (2010).
  • M. Mursaleen and K. Sharma Sunil, Spaces of I-convergeent sequences, Article ID 134534, 6 pages http://dx.doi. org/10.1155/2014/134534 (2014).
  • H. Nakano, Concave modulars, J. Math Soc. Japan, 5, 29-49 (1953).
  • W. H. Ruckle, n perfect symmetric BK-spaces, Math. Ann., 175, 121-126 (1968).
  • W. H. Ruckle, Symmetric coordinate spaces and symmetric bases, Canad. J. Math., 19, 828-838 (1967).
  • W. H. Ruckle, FK-spaces in which the sequence of coordinate vector is bounded, Canad. J. Math., 25, No. 5, 973-975 (1973).
  • T. Salat, On statistical convergent sequences of real numbers, Math, Slovaca, 30(1980).
  • T. Salat, B. C. Tripathy and M. Ziman, On some properties of I-convergence, Tatra Mt. math. Publ., 28, 279-286 (2004).
  • T. Salat, B. C. Tripathy and M. Ziman, On I-convergence field, Ital. J. Pure Appl. Math., 17, 45-54 (2005). [ I. J. Schoenberg,The integrability of certain functions and related summability methods, Amer.Math.Monthly, 66, 361-375 (1959). M. Sengonul and A. Eryilmaz, On the sequence spaces of interval numbers, Thai J. of Mathematics, 8, No. 3, 503-510 (2010).
  • B. C. Tripathy, On Statistical convergence, Proc. Estonian Acad. Sci. Phy. Math. Analysis, 299-303 (1998).
  • B. C. Tripathy and B. Hazarika, Paranorm I-convergent sequence spaces, Math. Slovaca, 59(2009), No. 4, 485-494 (2009).
  • B. K. Tripathy, B. C. Tripathy, On I-convergent double sequence, Soochow J. Math., 31(4) 549-560 (2005).
  • Yilmaz Yilmaz, Sumeyye Cakan and Sahika Aytekin, Topological quasilinear spaces, Hindawi Publishing Corporation, Abstract and Applied Analysis, (2012).

Year 2016, Volume: 4 Issue: 2, 125 - 137, 01.03.2016

Vakeel A. Khan Ayhan Esi Yasmeen Yasmeen Hira Fatima

Abstract

References

  • E. Ayhan and B. Hazarika, Some I-convergent of duoble ∧-interval number sequences defined by Orlicz function, Global, J. of Mathmatical Analysis,1,No. 3,110-116 (2013).
  • E. Ayhan, -sequence spces of interval numbers, Appl.Math. Inf., 8, No. 3, 1099-1102 (2014).
  • R. C. Buck, Generalized asymptotic density, Amer., J. Math.,75 , 335-346 (1953).
  • K. P. Chiao, Fundamental properties of interval vector max-norm, Tamsui Oxford Journal of Mathematical Science, 18, No. 2, 219-233 (2002).
  • P. S. Dwyer, Linear computation, New York, Wiley, (1951).
  • H. Fast, Sur la convergence statistique, Colloq. Math.,2, 241-244 (1951).
  • J. A. Fridy, On statistical convergence, Analysis, 5, 301-313 (1985).
  • V. A. Khan, mohd. Shafiq and K. Ebadullah, On paranorm I-convergent sequence spaces of interval numbers, J. of Nonlinear analysis and Optimisation (Theory and Application), 5, No. 1, 103-114 (2014).
  • V. K. Khan, Ahyan Esi. and Mohd. Shafiq, On paranorm BVI-convergent sequence spaces defined by an Orlicz function, Global Journal of Mathematical Analysis, 2, No. 2, 28-43 (2014).
  • V. A. Khan and Mohd. Shafiq, On some generalized I-convergent sequence spaces of interval numbers, 10, No. 3,00-00 (2014).
  • V. A. Khan, Suthep Suantai and K. Ebadullah, On some I-convergent sequence spaces defined by a sequence of modulii, J. of Nonlinear analysis and Optimisation, 3, No. 2, 145-152 (2012).
  • E. Kolk, On strong boundedness and summability with respect to a sequence of moduli, Acta Comment. Univ. Tartu., 960, 41-50 (1993).
  • E. Kolk, Inclusion theorems for some sequence spaces defined by a sequence of moduli, Acta Comment. Univ. Tartu., 970 65-72 (1994).
  • P. Kostyrko, M. Macaj and T. Salat, Statistical convergence and I- convergence, Real Analysis Exchange.
  • P. Kostyrko, T. Salat and W. Wilczynski, I-convergence, Real Analysis Exchange 26, No. 2, 669-686 (2000).
  • R. E. Moore, Automatic error analysis in digital computation, LSMD-48421, Lockheed Missiles and Space Company, (1959). R. E.Moore and C. T. Yang, Interval Analysis I, LMSD-285875, Lockheed Missiles and Space Company, Palo Alto, Calif., (1959).
  • M. Mursaleen and K. Noman Abdullah, On the spaces of -convergent and bounded sequences, Thai Journal of Mathematics, 8, No. 2, 311-329 (2010).
  • M. Mursaleen and K. Sharma Sunil, Spaces of I-convergeent sequences, Article ID 134534, 6 pages http://dx.doi. org/10.1155/2014/134534 (2014).
  • H. Nakano, Concave modulars, J. Math Soc. Japan, 5, 29-49 (1953).
  • W. H. Ruckle, n perfect symmetric BK-spaces, Math. Ann., 175, 121-126 (1968).
  • W. H. Ruckle, Symmetric coordinate spaces and symmetric bases, Canad. J. Math., 19, 828-838 (1967).
  • W. H. Ruckle, FK-spaces in which the sequence of coordinate vector is bounded, Canad. J. Math., 25, No. 5, 973-975 (1973).
  • T. Salat, On statistical convergent sequences of real numbers, Math, Slovaca, 30(1980).
  • T. Salat, B. C. Tripathy and M. Ziman, On some properties of I-convergence, Tatra Mt. math. Publ., 28, 279-286 (2004).
  • T. Salat, B. C. Tripathy and M. Ziman, On I-convergence field, Ital. J. Pure Appl. Math., 17, 45-54 (2005). [ I. J. Schoenberg,The integrability of certain functions and related summability methods, Amer.Math.Monthly, 66, 361-375 (1959). M. Sengonul and A. Eryilmaz, On the sequence spaces of interval numbers, Thai J. of Mathematics, 8, No. 3, 503-510 (2010).
  • B. C. Tripathy, On Statistical convergence, Proc. Estonian Acad. Sci. Phy. Math. Analysis, 299-303 (1998).
  • B. C. Tripathy and B. Hazarika, Paranorm I-convergent sequence spaces, Math. Slovaca, 59(2009), No. 4, 485-494 (2009).
  • B. K. Tripathy, B. C. Tripathy, On I-convergent double sequence, Soochow J. Math., 31(4) 549-560 (2005).
  • Yilmaz Yilmaz, Sumeyye Cakan and Sahika Aytekin, Topological quasilinear spaces, Hindawi Publishing Corporation, Abstract and Applied Analysis, (2012).
There are 29 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Vakeel A. Khan

Ayhan Esi This is me

Yasmeen Yasmeen This is me

Hira Fatima This is me

Publication Date March 1, 2016
Published in Issue Year 2016 Volume: 4 Issue: 2

Cite

APA Khan, V. A., Esi, A., Yasmeen, Y., Fatima, H. (2016). On some generalised I-convergent sequence spaces of double interval numbers. New Trends in Mathematical Sciences, 4(2), 125-137.
AMA Khan VA, Esi A, Yasmeen Y, Fatima H. On some generalised I-convergent sequence spaces of double interval numbers. New Trends in Mathematical Sciences. March 2016;4(2):125-137.
Chicago Khan, Vakeel A., Ayhan Esi, Yasmeen Yasmeen, and Hira Fatima. “On Some Generalised I-Convergent Sequence Spaces of Double Interval Numbers”. New Trends in Mathematical Sciences 4, no. 2 (March 2016): 125-37.
EndNote Khan VA, Esi A, Yasmeen Y, Fatima H (March 1, 2016) On some generalised I-convergent sequence spaces of double interval numbers. New Trends in Mathematical Sciences 4 2 125–137.
IEEE V. A. Khan, A. Esi, Y. Yasmeen, and H. Fatima, “On some generalised I-convergent sequence spaces of double interval numbers”, New Trends in Mathematical Sciences, vol. 4, no. 2, pp. 125–137, 2016.
ISNAD Khan, Vakeel A. et al. “On Some Generalised I-Convergent Sequence Spaces of Double Interval Numbers”. New Trends in Mathematical Sciences 4/2 (March 2016), 125-137.
JAMA Khan VA, Esi A, Yasmeen Y, Fatima H. On some generalised I-convergent sequence spaces of double interval numbers. New Trends in Mathematical Sciences. 2016;4:125–137.
MLA Khan, Vakeel A. et al. “On Some Generalised I-Convergent Sequence Spaces of Double Interval Numbers”. New Trends in Mathematical Sciences, vol. 4, no. 2, 2016, pp. 125-37.
Vancouver Khan VA, Esi A, Yasmeen Y, Fatima H. On some generalised I-convergent sequence spaces of double interval numbers. New Trends in Mathematical Sciences. 2016;4(2):125-37.
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