Cakalli, HuseyinMucuk, Osman2024-07-122024-07-1220162217-3412https://hdl.handle.net/20.500.12415/8220A 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.eninfo:eu-repo/semantics/closedAccessSummabilitylacunary statistical convergenceboundedness and continuityArticle232127WOS:000381995200002N/A