Weak and Strong Convergence Theorems of Quasi-Nonexpansive Mappings in a Hilbert Spaces

Gang Eun Kim ()
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Gang Eun Kim: Pukyong National University

Journal of Optimization Theory and Applications, 2012, vol. 152, issue 3, No 10, 727-738

Abstract: Abstract In this paper, we first prove the weak convergence for the Moudafi’s iterative scheme of two quasi-nonexpansive mappings. Then we prove the weak convergence for the Moudafi’s iterative scheme of quasi-nonexpansive mapping and nonexpansive mapping. Finally, we prove the strong convergence for the Moudafi’s iterative scheme of two quasi-nonexpansive mappings. Our results generalize the recent results due to Iemoto and Takahashi.

Keywords: Weak and strong convergence; Fixed point; Moudafi iteration process; Quasi-nonexpansive mapping (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s10957-011-9924-1

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