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A general iteration scheme for variational inequality problem and common fixed point problems of nonexpansive mappings in q-uniformly smooth Banach spaces

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  • Yanlai Song
  • Luchuan Ceng

Abstract

In this paper, we introduce a general iterative algorithm for finding a common element of the set of common fixed points of an infinite family of nonexpansive mappings and the set of solutions of systems of variational inequalities for two inverse strongly accretive mappings in a q-uniformly smooth Banach space. Then, we prove a strong convergence theorem for the iterative sequence generated by the proposed iterative algorithm under very mild conditions. The methods in the paper are novel and different from those in the early and recent literature. Our results can be viewed as improvement, supplementation, development and extension of the corresponding results in some references to a great extent. Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • Yanlai Song & Luchuan Ceng, 2013. "A general iteration scheme for variational inequality problem and common fixed point problems of nonexpansive mappings in q-uniformly smooth Banach spaces," Journal of Global Optimization, Springer, vol. 57(4), pages 1327-1348, December.
    • Handle: RePEc:spr:jglopt:v:57:y:2013:i:4:p:1327-1348
    DOI: 10.1007/s10898-012-9990-4
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    1. Lu-Chuan Ceng & Chang-yu Wang & Jen-Chih Yao, 2008. "Strong convergence theorems by a relaxed extragradient method for a general system of variational inequalities," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 67(3), pages 375-390, June.
    2. W. Takahashi & M. Toyoda, 2003. "Weak Convergence Theorems for Nonexpansive Mappings and Monotone Mappings," Journal of Optimization Theory and Applications, Springer, vol. 118(2), pages 417-428, August.
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    Cited by:

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    2. Yanlai Song & Mihai Postolache, 2021. "Modified Inertial Forward–Backward Algorithm in Banach Spaces and Its Application," Mathematics, MDPI, vol. 9(12), pages 1-17, June.

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