Int. Journal of Math. Analysis, Vol. 3, 2009, no. 24, 1199 - 1206 Common Fixed Point Theorems for Weakly Compatible Mappings on Menger Space and Application H. K. Pathak School of Studies in Mathematics Pt. Ravi Shankar Shukla University Raipur, 492010 (C.G.), India hkpathak@sify.com R. K. Verma 1 Department of Mathematics Govt. C. L. C. College Patan, Dist.-Durg, 491111 (C.G.), India rohitverma1967@sify.com Abstract The concept of weakly compatible mappings, defined in the Menger PM-space by Singh and Jain ([11]), is used to prove some common fixed point results. We ‘translate’ our fixed point theorem of this space into the metric space by an interesting way. The theorem thus obtained is a generalization of the main Theorem 3.3 of Jachymski [4]. Mathematics Subject Classification: 47H10, 54H25 Keywords: Compatible mapping, distribution function, Menger space, PM-space, specific distribution function, t-norm, weakly compatible mappings 1 Introduction The study of probabilistic metric space, as a milestone development, was extended and turned to the direction of fixed point theory by Sahgal and Bharucha-Reid [12]. In which they studied the Banach contraction principle of metric space into the complete Menger space. For, they introduced the concept of B-contraction maps in probabilistic metric spaces, and proved that 1 Corresponding Author