On sequences in 2-normed spaces

2013/06/11 by Ersan, Sibel, Cakalli, Huseyin
#40A05 #40A30 #46A70 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1306.2469

Abstract

A function f defined on a 2-normed space (X,||.,.||) is ward continuous if it preserves quasi-Cauchy sequences where a sequence (x_n) of points in X is called quasi-Cauchy if lim_n→∞||Δx_n,z||=0 for every z∈ X. Some other kinds of continuties are also introduced via quasi-Cauchy sequences in 2-normed spaces. It turns out that uniform limit of ward continuous functions is again ward continuous.

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