University of MaraghehSahand Communications in Mathematical Analysis2322-580706120170401A generalization of Kannan and Chatterjea fixed point theorems on complete $b$-metric spaces77862383110.22130/scma.2017.23831ENHamid FarajiDepartment of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran.Kourosh NourouziFaculty of Mathematics, K. N. Toosi University of Technology, P.O. Box 16315-1618, Tehran, Iran.Journal Article20161123In this paper, we give some results on the common fixed point of self-mappings defined on complete $b$-metric spaces. Our results generalize Kannan and Chatterjea fixed point theorems on complete $b$-metric spaces. In particular, we show that two self-mappings satisfying a contraction type inequality have a unique common fixed point. We also give some examples to illustrate the given results.http://scma.maragheh.ac.ir/article_23831_6c258f4180145f5370b887cf815cd897.pdf