Savas, EkremCakalli, HuseyinAshyralyev, A; Lukashov, A2024-07-122024-07-122016978-0-7354-1417-40094-243X10.1063/1.49596712-s2.0-85000774266https://dx.doi.org/10.1063/1.4959671https://hdl.handle.net/20.500.12415/89613rd International Conference on Analysis and Applied Mathematics (ICAAM) -- SEP 07-10, 2016 -- Almaty, KAZAKHSTANAn ideal I is a family of subsets of N, the set of positive integers which is closed under taking finite unions and subsets of its elements. A sequence (x(k)) of real numbers is said to be S(I)-statistically convergent to a real number L, if for each epsilon > 0 and for each delta > 0 the set {n is an element of N: 1/n {k <= n: vertical bar x(k) - L vertical bar >= epsilon}vertical bar >= delta} belongs to I. We introduce S(I)-statistically ward compactness of a subset of R, the set of real numbers, and S(I)-statistically ward continuity of a real function in the senses that a subset E of R is S(I)-statistically ward compact if any sequence of points in E has an S(I)-statistically quasi Cauchy subsequence, and a real function is S(I)-statistically ward continuous if it preserves S(I)-statistically quasi-Cauchy sequences where a sequence (x(k)) is called to be S(I)-statistically quasi-Cauchy when (Delta x(k)) is S(I)-statistically convergent to 0. We obtain results related to S(I)-statistically ward continuity, S(I)-statistically ward compactness, N-theta-ward continuity, and slowly oscillating continuity.eninfo:eu-repo/semantics/closedAccessSequencesIdeal convergenceCompactnessContinuityConference ObjectN/A1759WOS:000383223000054N/A