Document Type : Research Paper
Department of Mathematics, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran.
Department of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran.
Department of Mathematics, Iran University of Science and Technology, Tehran, Iran.
Recently Samet et al. introduced the notion of $\alpha$-$\psi$-contractive type mappings and established some fixed point theorems in complete metric spaces. In this paper, we introduce $\alpha$-$(\psi,\varphi)$-contractive mappings and stablish coincidence and common fixed point theorems for two mapping in complete metric spaces. We present some examples to illustrate our results. As application, we establish an existence and uniqueness theorem for a solution of some integral equations.