A new variation on lacunary statistical quasi Cauchy sequences

In this paper, the concept of an Sθ-δ2-quasi-Cauchy sequence is investigated. In this investigation, we proved interesting theorems related to Sθ-δ2-ward continuity, and some other kinds of continuities. A real valued function f defined on a subset A of R, the set of real numbers, is called Sθ-δ2-wa...

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Bibliographic Details
Main Author: Yildiz, Sebnem
Format: Conference Proceeding
Language:English
Subjects:
Continuity (mathematics)
Real numbers
Online Access:Get full text
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Summary:In this paper, the concept of an Sθ-δ2-quasi-Cauchy sequence is investigated. In this investigation, we proved interesting theorems related to Sθ-δ2-ward continuity, and some other kinds of continuities. A real valued function f defined on a subset A of R, the set of real numbers, is called Sθ-δ2-ward continuous on A if it preserves Sθ-δ2-quasi-Cauchy sequences of points in A, i.e. (f(αk)) is an Sθ-δ2-quasi-Cauchy sequence whenever (αk) is an Sθ-δ2-quasi-Cauchy sequence of points in A, where a sequence (αk) is called Sθ-δ2-quasi-Cauchy if (Δ2αk) is an Sθ-quasi-Cauchy sequence. It turns out that the set of Sθ-δ2-ward continuous functions is a closed subset of the set of continuous functions.
ISSN:0094-243X
1551-7616
DOI:10.1063/1.5043979