Variations on Rho statistical quasi Cauchy sequences

Cakalli, Huseyin

doi:10.1063/1.5095095

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2019

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Cited by 17 publications

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“…The author acknowledges that some of the results were presented at the 2nd International Conference of Mathematical Sciences, 31 July 2018-6 August 2018, (ICMS 2018) Maltepe University, Istanbul, Turkey, and the statements of some results in this paper will be appeared in AIP Conference Proceeding of 2nd International Conference of Mathematical Sciences, (ICMS 2018) Maltepe University, Istanbul, Turkey ( [15]).…”

Section: Acknowledgmentsmentioning

confidence: 97%

A new variation on statistically quasi Cauchy sequences

Cakalli¹

2018

AIP Conference Proceedings

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A sequence (α k ) of points in R, the set of real numbers, is called ρ-statistically p quasi Cauchy iffor each ε > 0, where ρ = (ρn) is a non-decreasing sequence of positive real numbers tending to ∞ such that lim sup n ρn n < ∞, ∆ρn = O(1), and ∆pα k+p = α k+p − α k for each positive integer k. A real-valued function defined on a subset of R is called ρ-statistically p-ward continuous if it preserves ρ-statistical p-quasi Cauchy sequences. ρ-statistical p-ward compactness is also introduced and investigated. We obtain results related to ρ-statistical p-ward continuity, ρ-statistical p-ward compactness, p-ward continuity, continuity, and uniform continuity.

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Section: Acknowledgmentsmentioning

confidence: 97%