A VARIATION ON LACUNARY STATISTICAL QUASI CAUCHY SEQUENCES

Abstract

In this paper, the concept of a lacunary statistically -quasi-Cauchysequence is investigated. In this investigation, we proved interesting theoremsrelated to lacunary statistically -ward continuity, and some other kinds ofcontinuities. A real valued function f defined on a subset A of R, the set ofreal numbers, is called lacunary statisticallyward continuous on A if it preserveslacunary statistically delta quasi-Cauchy sequences of points in A, i.e.(f( k)) is a lacunary statistically delta quasi-Cauchy sequence whenever ( k)is a lacunary statistically delta quasi-Cauchy sequence of points in A, wherea sequence ( k) is called lacunary statistically delta quasi-Cauchy if ( k) isa lacunary statistically quasi-Cauchy sequence. It turns out that the set oflacunary statisticallyward continuous functions is a closed subset of the setof continuous functions.