Common Fixed Point Theorems For Weakly Compatible Mappings Satisfying Rational Contractive Conditions In Complete Metric Spaces

By using notions of compatibility, weak compatibility and commutativity, Goyal ([5], [6]) prove some common fixed point theorems for six mappings involving rational contractive conditions in complete metric spaces. In this paper , we prove a common fixed point theorem for three pairs of weakly compatible mappings in complete metric spaces satisfying a rational inequality without any continuity requirement which generalize several previously known results due to Imdad and Ali [12], Goyal [5], Imdad-Khan [13], Jeong-Rhoades [7] and others.