| A Weak Convergence Theorem for Equilibrium Problems, Variational Inequalities and Fixed Point Problems in 2-Uniformly Convex Banach Spaces |
| Received:June 02, 2009 Revised:September 15, 2009 |
| Key Words:
relatively nonexpansive mapping $\alpha$-inversely strongly monotone operator equilibrium problem variational inequality weak convergence fixed point.
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant No.11071053), the Natural Science Foundation of Hebei Province (Grant No.A.2010001482) and the Project of Science and Research of Hebei Education Department (the second round in 2010). |
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| Abstract: |
| In this paper, we introduce a new iterative scheme for finding the common element of the set of solutions of an equilibrium problem, the set of solutions of variational inequalities for an $\alpha$-inversely strongly monotone operator and the set of fixed points of relatively nonexpansive mappings in a real uniformly smooth and 2-uniformly convex Banach space. Some weak convergence theorems are obtained, to extend the previous work. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2011.03.022 |
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