Abstract
In this paper, an iteration scheme for continuous pseudocontractive multi-valued mappings is introduced. The strong convergence of this iteration scheme is proved in reflexive real Banach spaces with a uniformly Gâteaux differentiable norm. This iteration scheme can be viewed as a multi-valued version of the corresponding one of Song and Chen [Y. Song, R. Chen, Convergence theorems of iterative algorithms for continuous pseudocontractive mappings, Nonlinear Anal. 67 (2007) 486–497].
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