In 1996 Kada, Suzuki and Takahashi defined the w-distance mappings on metric spaces and they proved fixed point theorems for w-distances. In 2008 Homidan, Ansari and Yao gave the Q-functions on quasi-metric space and they generalized the main results of Kada et al., since every w-distance is a Q-function. In 2011 Marin, Romaguera and Tirado introduced the generalization of Q-functions to T0 quasipseudometric spaces and they gave a new fixed point theorem for T0 quasipseudometric spaces by using Bianchini-Grandolfi gauge functions. In this paper the generalization of fixed point theorems for multivalued maps via Q-functions on complete T0 quasipseudometric spaces are investigated. Also, the conclusions related to previous theorems in this field are given.  

Keywords - .....

[1] Al-Homidan, S., Ansari, Q. H. and Yao, J. C., Some generalizations of Ekeland-type variational principle with applications to equilibrium problems and fixed point theory. Nonlinear Analysis: Theory, Methods and Applications, 69(1), 2008, 126-139.
[2] Kada, O., Suzuki, T. and Takahashi, W., Nonconvex minimization theorems and fixed point theorems in complete metric spaces. Mathematica japonicae, 44(2), 1996, 381-391.
[3] Latif, A. and Al-Mezel, S. A., Fixed point results in quasimetric spaces. Fixed Point Theory and Applications, 2011(1), 2011, 178306.
[4] Marn, J., Romaguera, S. and Tirado, P., Q-Functions on Quasimetric Spaces and Fixed Points for Multivalued Maps. Fixed Point Theory and Applications, 2011(1), 2011, 603861.