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Yayın On downward half Cauchy sequences(Elsevier B.V., 2018) Cakalli H.In this paper, we introduce and investigate the concepts of down continuity and down compactness. A real valued function f on a subset E of R, the set of real numbers is down continuous if it preserves downward half Cauchy sequences. It turns out that the set of down continuous functions is a proper subset of the set of continuous functions. © 2018 Elsevier B.V.Yayın A variation on strong lacunary quasi-Cauchy sequences in 2-normed spaces(American Institute of Physics Inc., 2015) Cakalli H.; Ersan S.In this paper, we introduce and investigate ideal strong lacunary ward continuity in 2-normed spaces. A function f on a subset A of a 2-normed space X into X is ideal strongly lacunary ward continuous if it preserves ideal strong lacunary quasi-Cauchy sequences of points in A. We also studied some other kinds of continuities. © 2015 AIP Publishing LLC.Yayın A variation on strongly lacunary ward continuity(Universitatii Al.I.Cuza din Iasi, 2016) Sonmez A.; Cakalli H.A function f defined on a subset A of a cone normed space X is strongly lacunary ward continuous if it preserves strongly lacunary quasi-Cauchy sequences of points in A; that is, (f (xk)) is a strongly lacunary quasi-Cauchy sequence whenever (xk) is strongly lacunary quasi-Cauchy. In this paper, not only strongly lacunary ward continuity, but also some other kinds of continuities are investigated in cone normed spaces. © 2016, Universitatii Al.I.Cuza din Iasi. All rights reserved.