Int. Journal of Math. Analysis, Vol. 2, 2008, no. 12, 551 - 555 Some Fixed Point Theorems in Compact Metric Space Ramakant Bhardwaj, S. S. Rajput * , Sanjay Choudhary ** and R.N.Yadava *** Department of Mathematics “TRUBA” Institute of Engineering and Information Technology Bhopal (M.P.), India ramakant_73@rediffmail, rkbhardwaj100@gmail.com * Head, Department of Mathematics Govt. P.G.Collage Gadarwara (M.P), India ** Head, Department of Mathematics Govt. Narmada P.G.Collage Hoshangabad (M.P), India *** Director Gr.Scientists & Head Resources Development Center R.R.L. Bhopal (M.P.), India Abstract In this paper, the concept of compact metric space and fixed point space has been introduced. We have proved some general fixed point theorems for self mapping setisfying a new contractive conditions in compact metric spaces, which generalised the result of Edelstein[2]. Mathematics Subject Classification: 54H25 Keywords: Fixed point, compact metric space