Strongly unfoldable, splitting and bounding

Assuming GCH $\mathsf {GCH}$ , we show that generalized eventually narrow sequences on a strongly inaccessible cardinal κ are preserved under one step iteration of the Hechler forcing for adding dominating κ-real. Moreover, if is unfoldable, 2 = + $2^\kappa =\kappa ^+$ and λ regular such < $\kappa ^+ \lambda$ then there set generic extension in which s ( ) b c $\mathfrak {s}(\kappa \kappa \mathfrak {b}(\kappa {c}(\kappa .