On $ \delta b $-open continuous functions

In this paper, we define an almost $ \delta b $-continuity, which is a weaker form of $ R $-map and we investigate and obtain its some properties and characterizations. Finally, we show that a function $ f:\left(X, \tau \right) \rightarrow \left(Y, \varphi \right) $ is almost $ \delta b $-continuous if and only if $ f:\left(X, \tau _{s}\right) \rightarrow \left(Y, \varphi _{s}\right) $ is $ b $-continuous, where $ \tau _{s} $ and $ \varphi _{s} $ are semiregularizations of $ \tau $ and $ \varphi $, respectively.