Two common fixed Point theorems for compatible mappings

Abstract

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