A new study on the strongly lacunary quasi Cauchyness
Huseyin Kaplan, Huseyin Cakalli

TL;DR
This paper introduces the concept of $N_{\theta}^{2}$ quasi-Cauchy sequences, explores their properties, and defines $N_{\theta}^{2}$ ward continuous functions that preserve such sequences, expanding the theory of quasi-Cauchy sequences.
Contribution
It defines and investigates $N_{\theta}^{2}$ quasi-Cauchy sequences and introduces $N_{\theta}^{2}$ ward continuity, a new form of sequence preservation in real analysis.
Findings
Established properties of $N_{\theta}^{2}$ quasi-Cauchy sequences
Proved theorems relating to $N_{\theta}^{2}$ ward continuous functions
Connected $N_{\theta}^{2}$ quasi-Cauchy sequences with existing sequence concepts
Abstract
In this paper, the concept of an quasi-Cauchy sequence is introduced. We proved interesting theorems related to -quasi-Cauchy sequences. A real valued function defined on a subset of , the set of real numbers, is ward continuous on if it preserves quasi-Cauchy sequences of points in , i.e. is an quasi-Cauchy sequence whenever is an quasi-Cauchy sequences of points in , where a sequence is called quasi-Cauchy if is an quasi-Cauchy sequence where for each positive integer .
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Taxonomy
TopicsApproximation Theory and Sequence Spaces · Advanced Banach Space Theory · Advanced Harmonic Analysis Research
