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Strong convergence theorems for variational inequality problems and fixed point problems in uniformly smooth and uniformly convex Banach spaces

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Abstract

In this paper, we introduce a new iterative algorithm for finding a common element of the set of solutions of a general variational inequality problem for finite inverse-strongly accretive mappings and the set of common fixed points for a nonexpansive mapping in a uniformly smooth and uniformly convex Banach space. We obtain a strong convergence theorem under some suitable conditions. Our results improve and extend the recent ones announced by many others in the literature.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, China

    Gang Cai & Shangquan Bu

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  1. Gang Cai
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  2. Shangquan Bu
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Correspondence to Gang Cai.

Additional information

This work was supported by the NSF of China (No. 11171172) and the Natural Science Foundation of Zhejiang Province (Q12A010097).

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Cai, G., Bu, S. Strong convergence theorems for variational inequality problems and fixed point problems in uniformly smooth and uniformly convex Banach spaces. J Glob Optim 56, 1529–1542 (2013). https://doi.org/10.1007/s10898-012-9923-2

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  • DOI: https://doi.org/10.1007/s10898-012-9923-2

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