Tbilisi Mathematical Journal

Spaces of strongly lacunary invariant summable sequences

E. Savaş

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

In this paper, we introduce and examine some properties of three sequence spaces defined using lacunary sequence and invariant mean which generalize several known sequence spaces.

Article information

Source
Tbilisi Math. J., Volume 13, Issue 1 (2020), 61-68.

Dates
Received: 20 September 2019
Accepted: 20 December 2019
First available in Project Euclid: 24 March 2020

Permanent link to this document
https://projecteuclid.org/euclid.tbilisi/1585015220

Digital Object Identifier
doi:10.32513/tbilisi/1585015220

Mathematical Reviews number (MathSciNet)
MR4079450

Zentralblatt MATH identifier
07200152

Subjects
Primary: 40B05: Multiple sequences and series (should also be assigned at least one other classification number in this section)
Secondary: 40C05: Matrix methods

Keywords
$\sigma$-convergence absolutely lacunary invariant and strongly lacunary invariant summability

Citation

Savaş, E. Spaces of strongly lacunary invariant summable sequences. Tbilisi Math. J. 13 (2020), no. 1, 61--68. doi:10.32513/tbilisi/1585015220. https://projecteuclid.org/euclid.tbilisi/1585015220


Export citation

References

  • G. Das and S. K. Mishra, Banach limits and lacunary strong almost convergence, J. Orissa Math. Soc. 2(2), (1983), 61-70.
  • A. R. Freedman, J. J. Sember and M. Rapheal, Some Cesaro-type summability spacces, Proc. London Math. Soc. (3) 37 (1973), 508-520.
  • B. Kuttner (1946), Note on strong summability, J. London Math. Soc. 21, 118-22.
  • G. G. Lorentz (1948), A contribution to the theory of divergent sequences, Acta Math. 80, 167-190.
  • I. J. Maddox, Spaces of strongly summable sequences, Quart. J. Math. Oxford Ser. (2) 18, 345-55.
  • I. J. Maddox and J. W. Roles, Absolute convexity in certain topological linear spaces, Proc. Camb. Philos. Soc. 66,(1969), 541-45.
  • I. J. Maddox (1970), Elements of Functional Analysis (Camb. Univ. Press).
  • Mursaleen, Matrix transformation between some new sequence spaces, Houston J. Math. 9(1993), 505–509.
  • Mursaleen, On some new invariant matrix methods of summability, Q.J. Math. 34 (1983), 77-86.
  • F. Nuray and E.Savas, Some new sequence spaces defined by a modulus function, Indian J. Pure Appl. Math., 24 (4), (1993), 657-663.
  • S. K. Saraswat and S. K. Gupta, Spaces of strongly $\sigma$-summable sequences, Bull. Cal. Math. Soc. 75,(1983), 179-184,
  • E. Savaş, A note on absolute $\sigma$ -summability, Istanbul Univ. Fac. Sci. Math. J. 50,(1991), 123-128.
  • E. Savaş,Invariant means and generalization of a theorem of S. Mishra, Doða Türk. J. Math. 14, (1989), 8-14.
  • E. Savaş, On strong $\sigma$-convergence, J. Orissa Math. Soc. Vol. 5, No.2, (1986), 45-53.
  • E. Savaş, On lacunary strong $\sigma$-convergence, Indian J. Pure Appl. Math., 21 (4), (1990), 359-365.
  • E. Savaş, Lacunary almost convergence and some new sequence spaces, Filomat 33 (5), (2019), 1397-1402.
  • P. Schaefer, Infinite matrices and invariant means, Proc. Amer. Math. Soc. 36(1972), 104–110.