Abstract
In this paper, the concept of a lacunary statistically -quasi-Cauchysequence is investigated. In this investigation, we proved interesting theoremsrelated to lacunary statisticallycontinuities. A real valued function f de…ned on a subset A of R, the set ofreal numbers, is called lacunary statisticallyserves lacunary 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 (a lacunary statistically quasi-Cauchy sequence. It turns out that the set oflacunary statisticallyof continuous functions
Highlights
The concept of continuity and any concept involving continuity play a very important role in pure mathematics and in other branches of sciences involving mathematics especially in computer science, information theory, economics, and biological science.Buck [2] introduced Cesaro continuity in 1946
We proved interesting theorems related to lacunary statistically -ward continuity, and some other kinds of continuities
Connor and Grosse-Erdman [20] have given sequential de...nitions of continuity for real functions calling G-continuity instead of A-continuity by means of a sequential method, or a method of sequential convergence, and their results cover the earlier works related to A-continuity where a method of sequential convergence, or brie‡y a method, is a linear function G de...ned on a linear subspace of all sequences of points in R denoted by cG, into R
Summary
The concept of continuity and any concept involving continuity play a very important role in pure mathematics and in other branches of sciences involving mathematics especially in computer science, information theory, economics, and biological science. A sequence ( k) of points in R, the set of real numbers, is called statistically convergent, or st-convergent to. A sequence ( k) of points in R is called to be lacunary statistically quasi-Cauchy if S lim k = 0, where k = k+1 k for each positive integer k. = (kr), a real valued function de...ned on a subset of R is lacunary statistically sequentially continuous if and only if it is ordinary sequentially continuous (see [13]). Where a function de...ned on a subset A of R is called lacunary statistically continuous or S continuous if it preserves S convergent sequences of points in A, i.e. A of R is called lacunary statistically ward continuous or S -ward continuous if it preserves S -quasi-Cauchy sequences of points in A, i.e. The purpose of this paper is to investigate the notion of lacunary statistically ward continuity and prove interesting theorems
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