Some new results and generalizations in metric fixed point theory

The main purpose of this paper is the study of the generalization of some results given in [M. Berinde, V. Berinde, On a general class of multi-valued weakly Picard mappings, J. Math. Anal. Appl. 326 (2007) 772–782] 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.