^{1}Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran.

^{2}Faculty of Mathematics, K. N. Toosi University of Technology, P.O. Box 16315-1618, Tehran, Iran.

Abstract

In 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.

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