A new study on the strongly lacunary quasi Cauchyness

2017/10/02 by Huseyin Kaplan, Kaplan, Huseyin, Huseyin Cakalli +1 · 1 citation
Mathematics · #26A15 #40A05 #40A30 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:26A15 #msc:40A05 #msc:40A30

paper · pdf · doi:10.48550/arxiv.1710.00515

11 pages

arxiv created 2017/10/02 · arxiv updated 2017/10/03

Abstract

In this paper, the concept of an N_θ² quasi-Cauchy sequence is introduced. We proved interesting theorems related to N_θ²-quasi-Cauchy sequences. A real valued function f defined on a subset A of ℝ, the set of real numbers, is N_θ² ward continuous on A if it preserves N_θ² quasi-Cauchy sequences of points in A, i.e. (f( α_k)) is an N_θ² quasi-Cauchy sequence whenever (α_k) is an N_θ² quasi-Cauchy sequences of points in A, where a sequence (α_k) is called N_θ² quasi-Cauchy if (Δ² α_k) is an N_θ quasi-Cauchy sequence where Δ²α_k=α_k+2-2α_k+1+α_k for each positive integer k.

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