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The purpose of this work is to study the following implicit iteration scheme xn=αnxn−1+(1−αn)Tnxn,n≥1, where Tn=TnmodN, and to prove several strongly convergent theorems of the iteration for a finite family of hemicontractive mappings in Banach space. Our results extend a recent result of Haiyun Zhou [Haiyun Zhou, Convergence theorems of common fixed points for a finite family of Lipschitz pseudocontractions...
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