| The purposes of this paper is to introduce the concepts of modified three-step iteration sequence with errors for a pair of mappings and three-step iteration sequence with errors for a pair of mappings. Some strong convergence theorems of modified three-step iteration sequences with errors with respect to asymptotically nonexpansive and strictly pseudocontractive mappings in Banach spaces are established. Strong convergence of three-step iteration sequence with errors for a pair of mappings involving nonexpansive mapping, -hemicontractive mapping and accretive operator, respectively, is also studied. Moreover two examples are given to show that our results are proper improvements of the results in [1, 3-15, 18, 20, 21, 32, 33, 36, 37, 39 ].
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