On lacunary strong \((A,u,\Delta^{m})\)-convergent sequences with respect to a sequence of modulus functions. (English) Zbl 1307.46002

Braha, N. L.; Esi, Ayhan; Loku, Valdete

Ilirias J. Math. 2, No. 1, 11-19 (2013).

Summary: The purpose of this paper is to define and study the spaces \(N_\theta(A,F,u,\Delta^m)\) and \(N^0_\theta(A,F,\) \(u,\Delta^m)\) of lacunary strong \((A,u,\Delta^m)\)-convergent sequences with respect to a sequence of modulus functions, where \(A=(a_{ik})\) is an infinite matrix of complex numbers. We also study some inclusion relations between lacunary strong \((A,u,\Delta^m)\)-convergence and lacunary \((A,u,\Delta^m)\)-statistical converence.
In the last section are shown the relationship between the above spaces and spaces defined by Cesàro summability methods \(N^c_\theta(A,F,u,\Delta^m)\) and \(N^{c0}_\theta(A,F,u,\Delta^m)\).

MSC:

46A45	Sequence spaces (including Köthe sequence spaces)
40C05	Matrix methods for summability
40A35	Ideal and statistical convergence

Keywords:

difference sequence; lacunary sequence; statistical convergence; sequence of modulus functions