In this paper, we present a fixed point theorem for multivalued mappings on generalized metric space in the sense of Jleli and Samet [M. Jleli, B. Samet, Fixed Point Theory Appl., 2015, 61 pages]. In fact, we obtain as a spacial case both b-metric version and dislocated metric version of Feng-Liu's fixed point result.

In the present paper, we introduce a new concept of (α, F d )-contraction on quasi metric space. Then we provide some new fixed point theorems for such type mappings on left K, left M and left Smyth-complete quasi metric spaces.