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The Mann‐Type Extragradient Iterative Algorithms with Regularization for Solving Variational Inequality Problems, Split Feasibility, and Fixed Point Problems

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  • Lu-Chuan Ceng
  • Himanshu Gupta
  • Ching-Feng Wen

Abstract

The purpose of this paper is to introduce and analyze the Mann‐type extragradient iterative algorithms with regularization for finding a common element of the solution set Ξ of a general system of variational inequalities, the solution set Γ of a split feasibility problem, and the fixed point set Fix(S) of a strictly pseudocontractive mapping S in the setting of the Hilbert spaces. These iterative algorithms are based on the regularization method, the Mann‐type iteration method, and the extragradient method due to Nadezhkina and Takahashi (2006). Furthermore, we prove that the sequences generated by the proposed algorithms converge weakly to an element of Fix(S)∩Ξ∩Γ under mild conditions.

Suggested Citation

  • Lu-Chuan Ceng & Himanshu Gupta & Ching-Feng Wen, 2013. "The Mann‐Type Extragradient Iterative Algorithms with Regularization for Solving Variational Inequality Problems, Split Feasibility, and Fixed Point Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:378750
    DOI: 10.1155/2013/378750
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    References listed on IDEAS

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    1. N. Nadezhkina & W. Takahashi, 2006. "Weak Convergence Theorem by an Extragradient Method for Nonexpansive Mappings and Monotone Mappings," Journal of Optimization Theory and Applications, Springer, vol. 128(1), pages 191-201, January.
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