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

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  • Zhao-Rong Kong
  • Lu-Chuan Ceng
  • Ching-Feng Wen

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.

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Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:975981
DOI: 10.1155/2012/975981
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