Abstract
The notion of a lacunary statistical d 2 -quasi-Cauchyness of sequence of real numbers is introduce and investigated. In this work, we present interesting theorems related to lacunary statistically d 2 -ward continuity. A function f, whose domain is included in R, and whose range included in R is called lacunary statistical d 2 ward continuous if it preserves lacunary statistical d 2 quasi-Cauchy sequences, i.e. (f(x k )) is a lacunary statistically d 2 quasi-Cauchy sequence whenever (x k ) is a lacunary statistically d 2 quasi-Cauchy sequence, where a sequence (x k ) is called lacunary statistically d 2 quasi-Cauchy if ( D 2 x k ) is a lacunary statistically quasi-Cauchy sequence. We find out that the set of lacunary statistical d 2 ward continuous functions is closed as a subset of the set of continuous functions.
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