Abstract:In this paper, we introduce the modified iterations of Mann's type for nonexpansive mapping and asymptotically nonexpansive mapping to have the strong and weak convergence in a uniformly convex Banach space. We also proved strong convergence theorems of our modified Mann's iteration processes for nonexpansive semigroups and asymptotically nonexpansive semigroups. The results presented in the paper give a partially affirmative answer to the open question raised by Kim and Xu (Nonlinear Anal. 64:1140-1152. Appl… Show more
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