Convergent triple sequences and statistical cluster points

Abstract

The concept of statistical convergence was introduced by Henry Fast (in the year 1951), which is an extension of the usual notion of convergence for real and complex number sequences. It is doubtless that the study of statistical convergence and its various generalizations has become an active research area. In particular, Kostyrko, Macaj and Sˇal´at (in 2000) introduced the interesting generalizations of statistical convergence by using the notion of ideals of subsets of positive integers. In this note, we investigate some problems concerning the sets of lacunary statistical cluster and λ-statistical cluster points of triple sequences via ideals in finite dimensional spaces, and some of its properties in finite dimensional Banach spaces are proved.