A Generalization of Nadler's Fixed Point Theorem

In the present paper, we generalize the well-known Nadler's fixed point theorem (Nadler in Pac J Math 30:475–488, 1969), and one of some Dhompongsa and Yingtaweesittikul type theorems for multi-valued operators, see (Dhompongsa and Yingtaweesittikul in Fixed Point Theory Appl, 2007). Also, we give an example showing that our result is a proper generalization of some previous theorems.