论文信息 - Lacunary statistical convergence.

Lacunary statistical convergence.

nIn this paper we study a related concept of convergence in which the set {k: k < n) is replaced by {k: kr-\ < k < kr}, for some lacunary sequence {kr} . The resulting summability method is compared to statistical convergence and other summability methods, and questions of uniqueness of the limit value are considered.

J. A. Fridy | C. Orhan | C. Orhan | J. Fridy | Cihan Orhan

[1] I. J. Maddox. A new type of convergence , 1978, Mathematical Proceedings of the Cambridge Philosophical Society.

[2] R. Creighton Buck,et al. Generalized Asymptotic Density , 1953 .

[3] J. A. Fridy,et al. ON STATISTICAL CONVERGENCE , 1985 .

[4] George G. Lorentz,et al. A contribution to the theory of divergent sequences , 1948 .

[5] Allen R. Freedman,et al. SOME CESARO-TYPE SUMMABILITY SPACES , 1978 .

[6] I. J. Schoenberg. The Integrability of Certain Functions and Related Summability Methods , 1959 .

[7] Allen R. Freedman,et al. Densities and summability. , 1981 .

[8] J. A. Fridy,et al. A MATRIX CHARACTERIZATION OF STATISTICAL CONVERGENCE , 1991 .

[9] H. Fast,et al. Sur la convergence statistique , 1951 .

[10] Jeff Connor,et al. On Strong Matrix Summability with Respect to a Modulus and Statistical Convergence , 1989, Canadian Mathematical Bulletin.

[11] J. S. Connor,et al. THE STATISTICAL AND STRONG p-CESARO CONVERGENCE OF SEQUENCES , 1988 .