Authors

• A. Razani
• M. Yazdi

Department of Mathematics, Faculty of Science, I. Kh. International University, P.O. Box: 34149-16818, Qazvin, Iran.

Abstract

Recently, Zhang and Song [Q. Zhang, Y. Song, Fixed point theory for generalized $varphi$-weak contractions, Appl. Math. Lett. 22(2009) 75-78] proved a common fixed point theorem for two maps satisfying generalized $\varphi$-weak contractions. In this paper, we prove a common fixed point theorem for a family of compatible maps. In fact, a new generalization of Zhang and Song's theorem is given.

Keywords

• Common fixed point
• Compatible mappings
• weakly compatible mappings
• $\varphi$-weak contraction
• Complete metric space