Viscosity Approximation With Weak Contractions for Fixed Point Problem Equilibrium Problem and Variational Inequality Problem

ZHANG Shi-sheng; LEE Heung-wing Joseph; CHAN Chi-kin; LIU Jing-ai

doi:10.3879/j.issn.1000-0887.2010.10.008

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ZHANG Shi-sheng, LEE Heung-wing Joseph, CHAN Chi-kin, LIU Jing-ai. Viscosity Approximation With Weak Contractions for Fixed Point Problem Equilibrium Problem and Variational Inequality Problem[J]. Applied Mathematics and Mechanics, 2010, 31(10): 1211-1219. doi: 10.3879/j.issn.1000-0887.2010.10.008

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Viscosity Approximation With Weak Contractions for Fixed Point Problem Equilibrium Problem and Variational Inequality Problem

doi: 10.3879/j.issn.1000-0887.2010.10.008

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

Received Date: 1900-01-01
Rev Recd Date: 2010-09-08
Publish Date: 2010-10-15

Abstract

Abstract

The purpose was by using the viscosity approximation method with a weak contraction to propose a modified 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 a finite family of equilibrium problems which was also a solution of a variational inequality.Under suitable conditions,some strong convergence theorems were established in the framework of Hilbert spaces.The results presented improve and extend the corresponding results in Colao, et al [Nonlinear Anal,2009, 71:27082715], Plubtieng, et al [J Math Anal Appl,2007, 336:455-469],Colao, et al [J Math Anal Appl, 2008, 344:340-352],Yao, et al [Fixed Point Theory Appl,2007, Art ID64363] and others.
- viscosity approximation with weak contraction mapping,
- equilibrium problem,
- nonex-pansive mapping,
- implicititeration,
- minimization problem

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References(12)

References

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