Delta quasi Cauchy sequences in metric spaces

In this extended abstract, we introduce the concept of delta quasi Cauchy sequences in metric spaces. A function f defined on a subset of a metric space X to X is called delta ward continuous if it preserves delta quasi Cauchy sequences, where a sequence (xk) of points in X is called delta quasi Cau...

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Bibliographic Details
Main Author: Cakalli, Huseyin
Format: Conference Proceeding
Language:English
Subjects:
Metric space
Sequences
Online Access:Get full text
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Summary:In this extended abstract, we introduce the concept of delta quasi Cauchy sequences in metric spaces. A function f defined on a subset of a metric space X to X is called delta ward continuous if it preserves delta quasi Cauchy sequences, where a sequence (xk) of points in X is called delta quasi Cauchy if limn→∞[d(xk+2,xk+1)−d(xk+1,xk)]=0. A new type compactness in terms of δ-quasi Cauchy sequences, namely δ-ward compactness is also introduced, and some theorems related to δ-ward continuity and δ-ward compactness are obtained. Some other types of continuities are also discussed, and interesting results are obtained.
ISSN:0094-243X
1551-7616
DOI:10.1063/5.0042190