Cakalli, HuseyinEt, MikailSengul, Hacer2024-12-242024-12-242016978-0-7354-1417-40094-243Xhttps://doi.org/10.1063/1.4959670https://hdl.handle.net/20.500.12604/57793rd International Conference on Analysis and Applied Mathematics (ICAAM) -- SEP 07-10, 2016 -- Almaty, KAZAKHSTANIn the present paper, we introduce a concept of ideal lacunary statistical quasi-Cauchy sequence of order alpha of real numbers in the sense that a sequence (x(k)) of points in R is called I lacunary statistically quasi-Cauchy of order alpha, if {r is an element of N : 1/h(r)(a) vertical bar Delta x(k)vertical bar >= epsilon vertical bar >= epsilon vertical bar >= delta}is an element of I for each epsilon > 0 and for each delta > 0, where an ideal I is a family of subsets of positive integers N which is closed under taking finite unions and subsets of its elements. The main purpose of this paper is to investigate ideal lacunary statistical ward continuity of order alpha, where a function f is called I lacunary statistically ward continuous of order alpha if it preserves I-lacunary statistically quasi-Cauchy sequences of order alpha, i.e. (f(x(n))) is a s(theta)(alpha)(I)-quasi-Cauchy sequence whenever (x(n)) is.eninfo:eu-repo/semantics/closedAccessSequencesIdeal convergenceCompactnessContinuityConference Object1759N/AWOS:000383223000053Q42-s2.0-8500036534410.1063/1.4959670