Abstract
References
- Aydin, B. Lacunary almost summability in certain linear topological spaces, Bull. Malays. Math. Sci. Soc. (2), 217–223, 2004.
- Banach, S. Th´eorie des operations lin´eaires(Warsaw, 1932).
- C¸ akan, C., Altay, B. and C¸ o¸skun, H. Double lacunary density and lacunary statistical con- vergence of double sequences, Studia Sci. Math. Hung. DOI:10.1556/SScMath.2009.1110.
- Freedman, A. R., Sember, J. J. and Raphael, M. Some Ces`aro type summability spaces, Proc. London Math. Soc. 37, 508–520, 1978.
- Lorentz, G. G. A contribution to the theory of divergent sequences, Acta Math. 80,167–190, 1948.
- Mursaleen, Some new invariant matrix methods of summability, Quart. J. Math. Oxford 34(2), 77–86, 1983.
- Mursaleen, Elements of Metric Spaces (Anamaya Publ., New Delhi, 2005).
- Schaefer, P. Infinite matrices and invariant means, Proc. Amer. Math. Soc. 36, 104- -110.
- Yosida, Y. Functional Analysis (Springer-Verlag, Berlin Heidelberg, New York, 1966).
Abstract
In this paper we define new sequence spaces Vσ(θ) and V ∞σ (θ) which are related to the concept of σ-mean and lacunary sequence θ = (kr), and characterize the matrix classes (l1, V ∞σ (θ)) and (l∞, V ∞σ (θ)).
Keywords
Lacunary sequence Matrix transformation Invariant mean Almost lacunary convergence 2000 AMS Classification: 40 C 05
References
- Aydin, B. Lacunary almost summability in certain linear topological spaces, Bull. Malays. Math. Sci. Soc. (2), 217–223, 2004.
- Banach, S. Th´eorie des operations lin´eaires(Warsaw, 1932).
- C¸ akan, C., Altay, B. and C¸ o¸skun, H. Double lacunary density and lacunary statistical con- vergence of double sequences, Studia Sci. Math. Hung. DOI:10.1556/SScMath.2009.1110.
- Freedman, A. R., Sember, J. J. and Raphael, M. Some Ces`aro type summability spaces, Proc. London Math. Soc. 37, 508–520, 1978.
- Lorentz, G. G. A contribution to the theory of divergent sequences, Acta Math. 80,167–190, 1948.
- Mursaleen, Some new invariant matrix methods of summability, Quart. J. Math. Oxford 34(2), 77–86, 1983.
- Mursaleen, Elements of Metric Spaces (Anamaya Publ., New Delhi, 2005).
- Schaefer, P. Infinite matrices and invariant means, Proc. Amer. Math. Soc. 36, 104- -110.
- Yosida, Y. Functional Analysis (Springer-Verlag, Berlin Heidelberg, New York, 1966).
Details
| Primary Language | English |
|---|---|
| Subjects | Statistics |
| Journal Section | Research Article |
| Authors | |
| Publication Date | March 1, 2009 |
| Published in Issue | Year 2009 Volume: 38 Issue: 3 |