Cakalli, Huseyin2024-07-122024-07-1220111521-1398https://hdl.handle.net/20.500.12415/8176A real function f is continuous if and only if (f(x(n))) is a convergent sequence whenever (x(n)) is convergent and a subset E of R is compact if any sequence x = (x(n)) of points in E has a convergent subsequence whose limit is in E where R is the set of real numbers. These well known results suggest us to introduce a concept of forward continuity in the sense that a function f is forward continuous if lim(n ->infinity)Delta(f) (x(n)) = 0 whenever lim(n ->infinity)Delta x(n) = 0 and a concept of forward compactness in the sense that a subset E of R is forward compact if any sequence x = (x.) of points in E has a subsequence z = (z(k)) = (x(nk)) of the sequence x such that lim(n ->infinity)Delta z(k)= 0 where Delta z(k) = z(k+1) z(k). We investigate forward continuity and forward compactness, and prove related theorems.eninfo:eu-repo/semantics/closedAccessContinuitysequencesseriessummabilitycompactnessArticle2302Q422513WOS:000288575900002Q4