Abstract
The definition of lacunary strongly convergence is extended to the definition of lacunary strong (A σ , p)-convergence with respect to invariant mean when A is an infinite matrix and p = (p i ) is a strictly positive sequence. We study some properties and inclusion relations.
Similar content being viewed by others
References
S. Banach: Theorie des operation lineaires. Warszava, 1932.
T. Bilgin: Strong A σ-summability defined by a modulus. J. Ist. Univ. Sci. 53 (1996), 89–95.
T. Bilgin: Lacunary strong A-convergence with respect to a modulus. Studia Univ. Babes-Bolyai Math. 46 (2001), 39–46.
G. Das and S. K. Mishra: Sublinear functional and a class of conservative matrices. J. Orissa Math. 20 (1989), 64–67.
G. Das and B. K. Patel: Lacunary distribution of sequences. Indian J. Pure Appl. Math. 20 (1989), 64–74.
A. R Freedman, J. J. Sember and M. Raphed: Some Cesaro-type summability spaces. Proc. London Math. Soc. 37 (1978), 508–520.
G. G. Lorentz: A contribution to the theory of divergent sequences. Acta Math. 80 (1980), 167–190.
Mursaleen: Matrix transformations between some new sequence spaces. Houston J. Math. 4 (1983), 505–509.
E. Ozturk and T. Bilgin: Strongly summable sequence spaces defined by a modulus. Indian J. Pure Appl. Math. 25 (1994), 621–625.
S. Pehlivan and B. Fisher: Lacunary strong convergence with respect to a sequence of modulus functions. Comment. Math. Univ. Carolin. 36 (1995), 69–76.
E. Savas: Lacunary strong σ-convergence. Indian J. Pure Appl. Math. 21 (1990), 359–365.
P. Scheafer: Infinite matrices and invariant meant. Proc. Amer. Math. Soc. 36 (1972), 104–110.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Bilgin, T. Lacunary Strong (A σ , p)-Convergence. Czech Math J 55, 691–697 (2005). https://doi.org/10.1007/s10587-005-0056-3
Received:
Issue Date:
DOI: https://doi.org/10.1007/s10587-005-0056-3