2012/04/09 by Hüseyi̇n Çakallı, Cakalli, Huseyin
Mathematics · #26A15 #40A05 #40A30 #42A65 #54C30 #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #General Mathematics (math.GM) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.1204.2445
openalex publication_date 2012/04/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we generalize the concept of a quasi-Cauchy sequence to a concept of a p-quasi-Cauchy sequence for any fixed positive integer p. For p=1 we obtain some earlier existing results as a special case. We obtain some interesting theorems related to p-quasi-Cauchy continuity, G-sequential continuity, slowly oscillating continuity, and uniform continuity. It turns out that a function f defined on an interval is uniformly continuous if and only if there exists a positive integer p such that f preserves p-quasi-Cauchy sequences where a sequence (xn) is called p-quasi-Cauchy if (xn+p-xn)n=1∞ is a null sequence.