a viscosity hybrid steepest descent method for generalized mixed equilibrium problems and variational inequalities for relaxed cocoercive mapping in hilbert spaces
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ID: 189172
2010
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Abstract
We present an iterative method for fixed point
problems, generalized mixed equilibrium problems, and
variational inequality problems. Our method is based
on the so-called viscosity hybrid steepest descent
method. Using this method, we can find the common
element of the set of fixed points of a nonexpansive
mapping, the set of solutions of generalized mixed
equilibrium problems, and the set of solutions of
variational inequality problems for a relaxed
cocoercive mapping in a real Hilbert space. Then, we
prove the strong convergence of the proposed iterative
scheme to the unique solution of variational
inequality. The results presented in this paper
generalize and extend some well-known strong
convergence theorems in the literature.
| Reference Key |
chantarangsi2010abstracta
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|---|---|
| Authors | ;Wanpen Chantarangsi;Chaichana Jaiboon;Poom Kumam |
| Journal | science and technology of advanced materials |
| Year | 2010 |
| DOI |
10.1155/2010/390972
|
| URL | |
| Keywords |
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