Summary: The main purpose of this paper is the study of the generalization of some results given in [M. Berinde
and V. Berinde
, J. Math. Anal. Appl. 326, No. 2, 772–782 (2007; Zbl 1117.47039
) and references therein]. Some generalizations of the Mizoguchi-Takahashi fixed point theorem, Kannan’s fixed point theorems and Chatterjea’s fixed point theorems are established by using our new fixed point theorems.