Abstract
In this paper, we introduce some new spaces of almost convergent sequences derived by Riesz mean and the lacunary sequence in a real n-normed space. By combining the definitions of lacunary sequence and Riesz mean, we obtain a new concept of statistical convergence which will be called weighted almost lacunary statistical convergence in a real n-normed space. We examine some connections between this notion with the concept of almost lacunary statistical convergence and weighted almost statistical convergence, where the base space is a real n-normed space.MSC:40C05, 40A35, 46A45, 40A05, 40F05.
Highlights
1 Introduction The concept of -normed space has been initially introduced by Gähler [ ]. This concept was generalized to the concept of n-normed spaces by Misiak [ ]
Statistical convergence has been generalized to the concept of a -normed space by Gürdal and Pehlivan [ ] and to the concept of an n-normed space by Reddy [ ]
We introduce some new spaces of almost convergent sequences derived by Riesz mean and lacunary sequence in a real n-normed space
Summary
The concept of -normed space has been initially introduced by Gähler [ ]. By combining the definitions of lacunary sequence and Riesz mean, we obtain a new concept of statistical convergence, which will be called weighted almost lacunary statistical convergence in a real n-normed space. The set of all almost convergent sequences and strongly almost convergent sequences with respect to the n-norm ·, · are denoted by F and [F], respectively, as follows: F = x ∈ l∞(X) : limk→∞ tkm(x – ξ e), z , .
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