Common fixed point theorems for families of weakly compatible maps (original) (raw)

In this paper the existence and approximation of a unique common fixed point of two families of weakly compatible self-maps on a complete metric space are investigated. An example is presented to show that our results for the mappings considered satisfying non-linear contractive type conditions are genuine generalizations of the recent result for metric spaces [B. Singh, S. Jain, A fixed point theorem in Menger space through weak compatibility, J. Math. Anal. Appl. 301 (2005) 439-448, Theorem 3.3] and many other known results. L.Ćirić et al. / Computers and Mathematics with Applications 55 (2008) 2533-2543 Jungck [7] generalized the notion of commuting maps by introducing the following notion of compatible mappings.