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, issue 1

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

Date: 2012
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https://doi.org/10.1155/2012/975981

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:975981

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