In this paper we present two new results for the existence of fixed points of multivalued mappings with closed values on quasi metric space. First we introduce the multivalued -contraction on quasi metric space
and give a fixed point result related to this concept. Then taking into account the
-function on a quasi metric space, we establish a
-function version of this concept as multivalued
-contraction and hence we present a fixed point result to see the effect of
-function to existence of fixed point of multivalued mappings on quasi metric space.