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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 Fd-contraction on quasi metric space (X; d) and give a fixed point result related to this concept. Then taking into account the Q-function on a quasi metric space, we establish a Q-function version of this concept as multivalued Fq-contraction and hence we present a fixed point result to see the effect of Q-function to existence of fixed point of multivalued mappings on quasi metric space. [ABSTRACT FROM AUTHOR]