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The purpose of this paper is to give a new modified Ishikawa type iteration algorithmfor common fixed points of total asymptotically strict pseudocontractive semigroups. Under the reduction of some conditions, both strong convergence and weak convergence of theiteration algorithm are proved in Banach spaces with new methods of proofs, respectively. The main results presented in this paper extend and improve the corresponding recentresults of many others

Convergence of a New Modified Ishikawa Type Iteration for Common Fixed Points of Total Asymptotically Strict Pseudocontractive Semigroups