Some Modified Extragradient Methods for Solving Split Feasibility and Fixed Point Problems

Zhao-Rong Kong, Lu-Chuan Ceng and Ching-Feng Wen

Abstract and Applied Analysis, 2012, vol. 2012, 1-32

Abstract:

We consider and study the modified extragradient methods for finding a common element of the solution set of a split feasibility problem (SFP) and the fixed point set of a strictly pseudocontractive mapping in the setting of infinite-dimensional Hilbert spaces. We propose an extragradient algorithm for finding an element of where is strictly pseudocontractive. It is proven that the sequences generated by the proposed algorithm converge weakly to an element of . We also propose another extragradient-like algorithm for finding an element of where is nonexpansive. It is shown that the sequences generated by the proposed algorithm converge strongly to an element of .

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:975981

DOI: 10.1155/2012/975981

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