Some Results on Variational Inclusion Problems and Fixed Point Problems With Applications

HAO Yan

doi:10.3879/j.issn.1000-0887.2009.12.010

Volume 30 Issue 12

Turn off MathJax

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2009 > 30(12): 1493-1500

HAO Yan. Some Results on Variational Inclusion Problems and Fixed Point Problems With Applications[J]. Applied Mathematics and Mechanics, 2009, 30(12): 1493-1500. doi: 10.3879/j.issn.1000-0887.2009.12.010

Citation:

PDF( 336 KB)

Some Results on Variational Inclusion Problems and Fixed Point Problems With Applications

doi: 10.3879/j.issn.1000-0887.2009.12.010

HAO Yan^1,2

1.
School of Mathematics Physics and Information Science, Zhejiang Ocean University, Zhoushan, Zhejiang 316004, P. R. China;

Received Date: 2009-05-31
Rev Recd Date: 2009-10-01
Publish Date: 2009-12-15

Abstract

Abstract

Based on a general iterative algorithm,the problem of approximating a common element in the solution set of quasi-variational inclusion problems and in the common fixed point set of an infinite family of nonexpansive mappings was considered.It is proved that the iterative sequences generated in the purposed iterative algorithm converges strongly to some common element in the framework of real Hilbert spaces.
- variational inequality,
- fixed point,
- nonexpansive mapping,
- quasi-variational inclusion

FullText(HTML)

References(10)

References

[1]	Chang S S. Set-valued variational inclusions in Banach spaces[J].J Math Anal Appl,2000,248(2):438-454. doi: 10.1006/jmaa.2000.6919
[2]	Noor M A,Noor K I. Sensitivity analysis for quasi-variational inclusions[J].J Math Anal Appl,1999,236(2):290-299. doi: 10.1006/jmaa.1999.6424
[3]	Zhang S S,Lee J H W,Chan C K. Algorithms of common solutions for quasi variational inclusion and fixed point problems[J].Appl Math Mech,2008,29(5):571-581. doi: 10.1007/s10483-008-0502-y
[4]	Chang S S, Lee H W J,Chan C K. A new method for solving equilibrium problem,fixed point problem and variational inequality problem with application to optimization[J].Nonlinear Anal,2009,70(9):3307-3319. doi: 10.1016/j.na.2008.04.035
[5]	Qin X,Shang M,Su Y. Strong convergence of a general iterative algorithm for equilibrium problems and variational inequality problems[J].Math Comput Modell,2008,48(7/8): 1033-1046. doi: 10.1016/j.mcm.2007.12.008
[6]	Xu H K. An iterative approach to quadratic optimization[J].J Optim Theory Appl,2003,116(3):659-678. doi: 10.1023/A:1023073621589
[7]	Shimoji K,Takahashi W. Strong convergence to common fixed points of infinite nonexpansive mappings and applications[J].Taiwanese J Math,2001,5(2):387-404.
[8]	Suzuki T. Strong convergence of Krasnoselskii and Mann's type sequences for one-parameter nonexpansive semigroups without Bochne integrals[J].J Math Anal Appl,2005,305(1): 227-239. doi: 10.1016/j.jmaa.2004.11.017
[9]	Pascali D,Sburlan S.Nonlinear Mappings of Monotone Type[M].Alphen aan den Rijn,Netherlands:Sythoff Noordhoff,1978.
[10]	Opial Z. Weak convergence of the sequence of successive approximations for nonexpansive mappings[J].Bull Amer Math Soc,1967,73(4):595-597.