In this paper the authors studied the problem of Sayyed and Badshah8 and prove common fixed point theorem in Hilbert Space. In recent years Rashwan and Sadik5, Malnge3, Berinde1, Rashwan4, Song and Chen¹¹, Cric, Ume and Khan² have studied the convergence of iterations to common fixed point for a pair of mappings. Rhoades6-7, proved the mappings T satisfying certain contractive condition, if the sequences of Mann iterates converged it converges to a fixed point of T. Sayyed and Badshah9-10 proved generalized contractive type mapping in Hilbert Space. AMS (2000) Subject Classifications: Primary 47H10, Secondary 54H25