LACUNARY STATISTICALLY UPWARD AND DOWNWARD HALF QUASI-CAUCHY SEQUENCES

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dc.authorid0000-0001-7344-5826en_US
dc.contributor.authorCakalli, Huseyin
dc.contributor.authorMucuk, Osman
dc.date.accessioned2024-07-12T21:50:54Z
dc.date.available2024-07-12T21:50:54Z
dc.date.issued2016en_US
dc.departmentMaltepe Üniversitesien_US
dc.description.abstractA real valued function defined on a subset E of R, the set of real numbers, is lacunary statistically upward continuous if it preserves lacunary statistically upward half quasi-Cauchy sequences where a sequence (x(k)) of points in R is called lacunary statistically upward half quasi Cauchy if lim(r infinity) 1/h(r) vertical bar{k is an element of I-r : x(k) - x(k+1) >= epsilon}vertical bar - 0 for every epsilon > 0; and (x(k)) is called lacunary statistically downward half quasi-Cauchy if lim(r ->infinity) 1/h(r) vertical bar {k is an element of I-r : x(k+1) - x(k) >= epsilon}vertical bar = 0 for every epsilon > 0, where theta = (k(r)) is an increasing sequence of non-negative integers such that k(0) = 1 and h(r) : k(r) - k(r-1) -> infinity. We investigate lacunary statistically upward continuity and lacunary statistically downward continuity and prove some interesting theorems. It turns out that not only a lacunary statistically upward continuous function on a below bounded subset, but also a lacunary statistically downward continuous function on an above bounded subset is uniformly continuous.en_US
dc.identifier.endpage23en_US
dc.identifier.issn2217-3412
dc.identifier.issue2en_US
dc.identifier.startpage12en_US
dc.identifier.urihttps://hdl.handle.net/20.500.12415/8220
dc.identifier.volume7en_US
dc.identifier.wosWOS:000381995200002en_US
dc.identifier.wosqualityN/Aen_US
dc.indekslendigikaynakWeb of Science
dc.language.isoenen_US
dc.publisherUNIV PRISHTINESen_US
dc.relation.ispartofJOURNAL OF MATHEMATICAL ANALYSISen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.snmzKY01962
dc.subjectSummabilityen_US
dc.subjectlacunary statistical convergenceen_US
dc.subjectboundedness and continuityen_US
dc.titleLACUNARY STATISTICALLY UPWARD AND DOWNWARD HALF QUASI-CAUCHY SEQUENCESen_US
dc.typeArticle
dspace.entity.typePublication

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