In this manuscript, we establish strong convergence results for the improved iteration methods introduced by Owojori and Imoru [7], to fixed points of hemicontractive operators. Our results in this paper are extensions of the results of: Ishikawa [4], Deng and Ding [3], Chidume [1], Chidume and Osilike [2], Owojori and Imoru [6], Qihou [8], Liu [5] and Xu [10] from the Mann and Ishikawa iteration methods, (with and without errors), to more general iteration methods and from Lipschitz or continuous pseudocontractive operators to slightly more general continuous hemicontractive operators.