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The Semi normed space defined~by~$\chi$~sequences

Year 2014, Volume: 2 Issue: 2, 125 - 128, 01.08.2014

Nagarajan Subramanıan Peruyannan. Thirunavukarasu Raman Babu

Abstract

In this paper we introduce the sequence spaces ( , , , ), Λ( , , , ) and define a semi normed space ( , ) semi normed by . We study some properties of these sequence spaces and obtain some inclusion relations

Keywords

Chi sequence Analytic sequence Invariant mean Semi norm

References

  • Y. Altin and M. Et, Generalized di_erence sequences spaces de_ned by a modulus function in a locally convex space, Soochow J. Math. 31(1) (2005), 233-243.
  • H. I. Brown, The summability _eld of a perfect l{l method of summation, J. Anal. Math., 20 (1967), 281-287.
  • R. Colak, M. Et, and E. Malkowsky, Some topics of sequence spaces, Lecture Notes in Mathematics, Firat University Press, Elazig, Turkey, 2004.
  • C. Go_man and G. Pedrick, First Course in Functional Analysis, Prentice Hall India, New Delhi, 1974.
  • P. K. Kamthan and M. Gupta, Sequence spaces and Series. Lecture Notes in Pure and Applied Mathematics, 65 Marcel Dekker, Inc., New York, 1981.
  • I. J. Maddox, Elements of Functional Analysis, Cambridge Univ. Press, 1970.
  • I. J. Maddox, Sequence spaces de_ned by a modulus, Math. Proc., Cambridge Philos. Soc. 100 (1986), 161-166.
  • H. Nakano, \Concave modulars", Journal of the Mathematical Society of Japan, 5(1) (1953), 29-49.
  • W. H. Ruckle, FK spaces in which the sequence of coordinate vectors is bounded, Canad. J. Math., 25 (1973), 973-978.
  • S. M. Sirajudeen, Matrix Transformation of Co(P), l∞(P), lP and l into χ, Indian J. Pure Appl. Math., 12(9), (1981), 1106-1113.
  • B. C. Tripathy, S. Mahanta and M. Et, On a class of generalized difference sequence space de_ned by modulus function, Hakkaido Math. Jour., XXXIV (3) (2005), 667{677.
  • A. Wilansky, Functional Analysis, Blaisdell Publishing Company, New York, 1964.
  • A. Wilansky, Summability through Functional Analysis, North Holland Mathematics Studies, North-Holland Publishing, Amsterdam, Vol. 85 (1984).

The semi normed space defined by sequences

Year 2014, Volume: 2 Issue: 2, 125 - 128, 01.08.2014

Nagarajan Subramanıan Peruyannan. Thirunavukarasu Raman Babu

Abstract

References

  • Y. Altin and M. Et, Generalized di_erence sequences spaces de_ned by a modulus function in a locally convex space, Soochow J. Math. 31(1) (2005), 233-243.
  • H. I. Brown, The summability _eld of a perfect l{l method of summation, J. Anal. Math., 20 (1967), 281-287.
  • R. Colak, M. Et, and E. Malkowsky, Some topics of sequence spaces, Lecture Notes in Mathematics, Firat University Press, Elazig, Turkey, 2004.
  • C. Go_man and G. Pedrick, First Course in Functional Analysis, Prentice Hall India, New Delhi, 1974.
  • P. K. Kamthan and M. Gupta, Sequence spaces and Series. Lecture Notes in Pure and Applied Mathematics, 65 Marcel Dekker, Inc., New York, 1981.
  • I. J. Maddox, Elements of Functional Analysis, Cambridge Univ. Press, 1970.
  • I. J. Maddox, Sequence spaces de_ned by a modulus, Math. Proc., Cambridge Philos. Soc. 100 (1986), 161-166.
  • H. Nakano, \Concave modulars", Journal of the Mathematical Society of Japan, 5(1) (1953), 29-49.
  • W. H. Ruckle, FK spaces in which the sequence of coordinate vectors is bounded, Canad. J. Math., 25 (1973), 973-978.
  • S. M. Sirajudeen, Matrix Transformation of Co(P), l∞(P), lP and l into χ, Indian J. Pure Appl. Math., 12(9), (1981), 1106-1113.
  • B. C. Tripathy, S. Mahanta and M. Et, On a class of generalized difference sequence space de_ned by modulus function, Hakkaido Math. Jour., XXXIV (3) (2005), 667{677.
  • A. Wilansky, Functional Analysis, Blaisdell Publishing Company, New York, 1964.
  • A. Wilansky, Summability through Functional Analysis, North Holland Mathematics Studies, North-Holland Publishing, Amsterdam, Vol. 85 (1984).
There are 13 citations in total.

Details

Journal Section Articles
Authors

Nagarajan Subramanıan This is me

Peruyannan. Thirunavukarasu This is me

Raman Babu This is me

Publication Date August 1, 2014
Published in Issue Year 2014 Volume: 2 Issue: 2

Cite

APA Subramanıan, N., Thirunavukarasu, P., & Babu, R. (2014). The Semi normed space defined~by~$\chi$~sequences. New Trends in Mathematical Sciences, 2(2), 125-128.
AMA Subramanıan N, Thirunavukarasu P, Babu R. The Semi normed space defined~by~$\chi$~sequences. New Trends in Mathematical Sciences. August 2014;2(2):125-128.
Chicago Subramanıan, Nagarajan, Peruyannan. Thirunavukarasu, and Raman Babu. “The Semi Normed Space defined~by~$\chi$~sequences”. New Trends in Mathematical Sciences 2, no. 2 (August 2014): 125-28.
EndNote Subramanıan N, Thirunavukarasu P, Babu R (August 1, 2014) The Semi normed space defined~by~$\chi$~sequences. New Trends in Mathematical Sciences 2 2 125–128.
IEEE N. Subramanıan, P. Thirunavukarasu, and R. Babu, “The Semi normed space defined~by~$\chi$~sequences”, New Trends in Mathematical Sciences, vol. 2, no. 2, pp. 125–128, 2014.
ISNAD Subramanıan, Nagarajan et al. “The Semi Normed Space defined~by~$\chi$~sequences”. New Trends in Mathematical Sciences 2/2 (August 2014), 125-128.
JAMA Subramanıan N, Thirunavukarasu P, Babu R. The Semi normed space defined~by~$\chi$~sequences. New Trends in Mathematical Sciences. 2014;2:125–128.
MLA Subramanıan, Nagarajan et al. “The Semi Normed Space defined~by~$\chi$~sequences”. New Trends in Mathematical Sciences, vol. 2, no. 2, 2014, pp. 125-8.
Vancouver Subramanıan N, Thirunavukarasu P, Babu R. The Semi normed space defined~by~$\chi$~sequences. New Trends in Mathematical Sciences. 2014;2(2):125-8.