Deferred statistically half quasi cauchy sequences

A sequence (xk) of points in R is called deferred statistically downward half quasi Cauchy if lim┬(n→∞)⁡〖1/((q(n)-p(n))) |p(n)0. A real valued function f defined on a subset E of R, the set of real numbers, is deferred statistically downward continuous if it preserves lacunary statistically downward half quasi Cauchy sequences, i.e. f(xk) is a deferred statistically downward half quasi Cauchy convergent sequence whenever (xk) is. In this thesis, we introduce the concept of deferred statistical downward continuity and deferred statistical downward compactness by using deferred statistical convergence and prove some theorems in first chapter. We introduce the concept of deferred statistical p-quasi Cauchy and deferred statistical p-quasi continuity and prove some theorems in second chapter.