Fixed points for directional multi-valued k(.)-contractions

A fixed point theorem for directional multi-valued k(.)-contractions acting m a complete metric space is established which extends similar results both for k(.)-contractions and directional contractions. Such theorem enables to obtain fixed points theorems for the former class of set-valued maps from those valid for the latter one without metrical convexity or proximinality assumptions, thereby contributing to unify the current setting of the theory. Connections with several recent advances on this subject are also examinated.