Abstract:In this study, we establish that both the Mann and Ishikawa iteration processes are T-stable for the mappings T satisfying a more general contractive definition than that of Osilike [1] . The results obtained generalize some of the recent results of Osilike [1] which are themselves generalizations and extensions of some of the results of Harder and Hicks [2] and Rhoades [3,4] .
Abstract:In this study, we establish some stability results for the Krasnoselskij and the Ishikawa iteration procedures. We employ the same method as in Berinde [1] , but using a more general contractive definition than those of Berinde [1] , Rhoades [2] , Harder and Hicks [3] and Osilike [4,5] .
Owojori and Imoru [1] introduced some iteration methods and investigated its convergence for pseudocontractive and accretive operators in arbitrary Banach spaces. In this work, strong convergence results are established for fixed points of a general type of quasicontractive mappings in arbitrary real Banach spaces. Our results here represent some improvements on the earlier results of Owojori and Imoru [1], Naimpally and Singh [2], Chidume [3, 4], Qihou [5], Ganguly and Bandyopahyay [6], Chidume and Osilike [7], Rhoades [8] and Osilike [9] for quasicontractive operators in Banach spaces
In this work, we establish strong convergence of the improved modified three-step iteration methods for asymptotically nonexpansive operators in uniformly smooth and convex Banach spaces. Our results generalize the previous results of Schu [10], Osilike and Aniagbosor [5], Xu and Noor [13], as well as Owojori and Imoru [7] among others
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