Coincidence and ‎C‎ommon Fixed Point Results for $\alpha$-$(\psi,\varphi)$-Contractive Mappings in Metric Spaces‎

Subject Areas : International Journal of Industrial Mathematics

J. Esmaily ¹ , S. M. Vaezpour ² , R. Saadati ³

1 - Department of Mathematics, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran.
2 - Department of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran.
3 - Department of Mathematics, Iran University of Science and Technology, Tehran, Iran.

Received: 2015-04-04 Accepted : 2015-09-18 Published : 2019-12-01

Keywords: Integral equations, $alpha-(psi, varphi)$-contraction, Common fixed point, Coincidence point,

Abstract :

‎‎‎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.‎