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Analysis Mathematica

, 37:173 | Cite as

On A-invariant mean and A-almost convergence

  • M. Mursaleen
Article

Abstract

The idea of A-invariant mean and A-almost convergence is due to J. P. Duran [8], which is a generalization of the usual notion of Banach limit and almost convergence. In this paper, we discuss some important properties of this method and prove that the space F(A) of A-almost convergent sequences is a BK space with ‖ · ‖, and also show that it is a nonseparable closed subspace of the space l of bounded sequences.

Keywords

Banach Space Sequence Space Cauchy Sequence Bounded Sequence Double Sequence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Об A-инвариантных средних и A-почти сходимости

Резуме

Идея A-инвариантных средних и A-почти сходимости принадлежит Дж. П. Дурану [8] и является обобщением принятых понятий Банахова предела и почти сходимости. В настоящей работе обсуждаются некоторые важные свойства этого метода и устанавливается, что пространство F(A) A-почти сходящихся после-довательностей является BK пространством с нормой ‖ · ‖, а также что оно есть несепарабельное эамкнутое подпространство пространства ограниченных последовательностей.

References

  1. [1]
    Z. U. Ahmad and M. Mursaleen, An application of Banach limits, Proc. Amer. Math. Soc., 103(1988), 244–246.MathSciNetzbMATHCrossRefGoogle Scholar
  2. [2]
    S. Banach, Théorie des operations liniaries, (Warszava, 1932).Google Scholar
  3. [3]
    F. Başar and M. Kirişçi, Almost convergence and generalized difference matrix, Comput. Math. Appl., 61(2011), 602–611.MathSciNetzbMATHCrossRefGoogle Scholar
  4. [4]
    G. Das, B. Kuttner, and S. Nanda, Some sequence spaces and absolute almost convergence, Trans. Amer. Math. Soc., 283(1984), 729–739.MathSciNetzbMATHCrossRefGoogle Scholar
  5. [5]
    G. Das, B. Kuttner, and S. Nanda, On absolute almost convergence, J. Math. Anal. Appl., 164(1992), 381–398.MathSciNetzbMATHCrossRefGoogle Scholar
  6. [6]
    G. Das and S. K. Mishra, A note on a theorem of Maddox on strong almost convergence, Math. Proc. Camb. Philos. Soc., 89(1981), 393–396.MathSciNetzbMATHCrossRefGoogle Scholar
  7. [7]
    G. Das, Banach and other limits, J. Lond. Math. Soc., 7(1973), 327–347.Google Scholar
  8. [8]
    J. P. Duran, Almost convergence, summability and ergodicity, Canad. J. Math., 26(1974), 372–387.MathSciNetzbMATHCrossRefGoogle Scholar
  9. [9]
    G. G. Lorentz, A contribution to theory of divergent sequences, Acta Math., 80(1948), 167–190.MathSciNetzbMATHCrossRefGoogle Scholar
  10. [10]
    I. J. Maddox, A new type of convergence, Math. Proc. Camb. Philos. Soc., 83(1978), 61–64.MathSciNetzbMATHCrossRefGoogle Scholar
  11. [11]
    F. Móricz and B. E. Rhoades, Almost convergence of double sequences and strong regularity of summability matrices, Math. Proc. Camb. Philos. Soc., 104(1988), 283–294.zbMATHCrossRefGoogle Scholar
  12. [12]
    M. Mursaleen, On some new invariant matrix methods of summability, Quart. J. Math. Oxford, 34(1983), 77–86.MathSciNetzbMATHCrossRefGoogle Scholar
  13. [13]
    M. Mursaleen, Absolute almost convergent sequences, Houston J. Math., 10(1984), 427–431.MathSciNetzbMATHGoogle Scholar
  14. [14]
    R. A. Raimi, Invariant means and invariant matrix methods on summability, Duke Math. J., 30(1963), 81–94.MathSciNetzbMATHCrossRefGoogle Scholar
  15. [15]
    P. Schaefer, Infinite matrices and invariant means, Proc. Amer. Math. Soc., 36(1972), 104–110.MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2011

Authors and Affiliations

  1. 1.Department of MathematicsAligarh Muslim UniversityAligarhIndia

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