Algorithms of Common Solutions for Quasi Variational Inclusion and Fixed Point Problems

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

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Article Navigation > Applied Mathematics and Mechanics > 2008 > 29(5): 515-524

ZHANG Shi-sheng, LEE Joseph H W, CHAN Chi Kin. Algorithms of Common Solutions for Quasi Variational Inclusion and Fixed Point Problems[J]. Applied Mathematics and Mechanics, 2008, 29(5): 515-524.

Citation:

ZHANG Shi-sheng, LEE Joseph H W, CHAN Chi Kin. Algorithms of Common Solutions for Quasi Variational Inclusion and Fixed Point Problems[J]. Applied Mathematics and Mechanics, 2008, 29(5): 515-524.

Citation:

ZHANG Shi-sheng, LEE Joseph H W, CHAN Chi Kin. Algorithms of Common Solutions for Quasi Variational Inclusion and Fixed Point Problems[J]. Applied Mathematics and Mechanics, 2008, 29(5): 515-524.

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Algorithms of Common Solutions for Quasi Variational Inclusion and Fixed Point Problems

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

Received Date: 2007-08-30
Rev Recd Date: 2008-03-19
Publish Date: 2008-05-15

Abstract

Abstract

The purpose is to present an iterative scheme for finding a common element of the set of solutions of the variational inclusion problem with multi-valued maximal monotone mapping and inverse-strongly monotone mappings and the set of fixed points of nonexpansive mappings in Hilbert space.Under suitable conditions,some strong convergence theorems for approximating to this common elements were proved.The results presented not only improve and extend the main results in Korpelevich[Ekonomika i Matematicheskie Metody,1976,12(4):747-756],but also extend and replenish the corresponding results in Iiduka and Takahashi[Nonlinear Anal,TMA,2005,61(3):341-350], Takahashi and Toyoda[J Optim Theory Appl,2003,118(2):417-428],Nadezhkina and Takahashi[J Optim Theory Appl,2006,128(1):191-201]and Zeng and Yao[Taiwanese Journal of Mathematics, 2006,10(5):1293-1303].
- variational inclusion,
- multi-valued maximal monotone mapping,
- inverse-strongly monotone mapping,
- metric projection,
- fixed point,
- nonexpansive mapping

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References(22)

References

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