Quadratic Minimization for Equilibrium Problem Variational Inclusion and Fixed Point Problem

ZHANG Shi-sheng; LEE Joseph H W; CHAN Chi-kin

doi:10.3879/j.issn.1000-0887.2010.07.013

Volume 31 Issue 7

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ZHANG Shi-sheng, LEE Joseph H W, CHAN Chi-kin. Quadratic Minimization for Equilibrium Problem Variational Inclusion and Fixed Point Problem[J]. Applied Mathematics and Mechanics, 2010, 31(7): 874-883. doi: 10.3879/j.issn.1000-0887.2010.07.013

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Quadratic Minimization for Equilibrium Problem Variational Inclusion and Fixed Point Problem

doi: 10.3879/j.issn.1000-0887.2010.07.013

1.
Department of Mathematics, Yibin University, Yibin, Sichuan 644007, P. R. China;

Received Date: 1900-01-01
Rev Recd Date: 2010-05-30
Publish Date: 2010-07-15

Abstract

Abstract

The purpose was by using the resolvent approach to find the solutions to the quad-raticminimization problem: min_x∈Ω||x||², where Ω was the intersection set of the set of solutions to some generalized equilibrium problem, the set of common fixed points for an infinite family of nonexpansive mappings and the set of solutions to some variational in clusions in the setting of Hilbert spaces. Under suitable conditions some new strong convergence theorems for approximating to a solution of the above minimization problem were proved.

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References

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