Some convergence results for fixed points of hemicontractive operators in some Banach spaces

Olusegun O. Owojori

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.