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.
Highlights
Introduction and BackgroundIn 1922, Banach de...ned normed linear spaces as a set of axioms
It is shown that a sequence is A-statistically Cauchy i¤ its A-statistical barrier is equal to zero
The ...rst notable attempt was by Vulich [41]
Summary
Introduction and BackgroundIn 1922, Banach de...ned normed linear spaces as a set of axioms. (a) A sequence (xn) in n-normed space (X; k:; :::; :k) is said to be Astatistically localized in the subset K X if the sequence kxn x; z1; z2; :::; zn 1k A-statistically converges for all x; z1; z2; :::; zn 1 2 K.
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