A-statistically localized sequences in n-normed spaces

Abstract

In 1974, Krivonosov defined the concept of localized sequence that is defined as a generalization of Cauchy sequence in metric spaces. In this present work, the A-statistically localized sequences in n-normed spaces are defined and some main properties of A-statistically localized sequences are given. Also, it is shown that a sequence is A-statistically Cauchy iff its A-statistical barrier is equal to zero. Moreover, we define the uniformly A-statistically localized sequences on n-normed spaces and investigate its relationship with A-statistically Cauchy sequences.

Keywords

• A-statistical convergence
• n-normed spaces
• A-statistical localor of the sequence

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