Kaplan, HuseyinCakalli, HuseyinAshyralyev, ALukashov, A2019-08-012019-08-012016978-0-7354-1417-40094-243Xhttps://dx.doi.org/10.1063/1.4959665https://hdl.handle.net/11480/37773rd International Conference on Analysis and Applied Mathematics (ICAAM) -- SEP 07-10, 2016 -- Almaty, KAZAKHSTANWe introduce a new function space, namely the space of N-theta(p)-ward continuous functions, which turns out to be a closed subspace of the space of continuous functions for each positive integer p. N-theta(alpha)(p)-ward continuity is also introduced and investigated for any fixed 0 < a <= 1, and for any fixed positive integer p. A real valued function f defined on a subset A of R, the set of real numbers is N-theta(alpha)(p)-ward continuous if it preserves N-theta(alpha)(p)-quasi-Cauchy sequences, i.e. (f(x(n))) is an N-theta(alpha)(p)-quasi--Cauchy sequence whenever (x(n)) is N-theta(alpha)(p)-quasi-Cauchy sequence of points in A, where a sequence (x(k)) of points in R is called N-theta(alpha)(p)-quasi-Cauchy if [GRAPHICS] 1/h(r)(alpha) [GRAPHICS] vertical bar Delta x(k)vertical bar(p) - 0, where Delta x(k) = x(k+1) - x(k) for each positive integer k, p is a fixed positive integer, alpha is fixed in ]0, 1], I-r = (k(r-1), k(r)], and theta = (k(r)) is a lacunary sequence, i.e. an increasing sequence of positive integers such that k(0) not equal 0, and h(r) : k(r) - k(r-1) -> infinity.eninfo:eu-repo/semantics/closedAccessStrongly lacunary convergenceQuasi-Cauchy sequencesContinuityConference Object175910.1063/1.49596652-s2.0-85000613520N/AWOS:000383223000048N/A