Some Results on Variational Inclusion Problems and Fixed Point Problems With Applications
-
摘要: 基于一个广义迭代算法,考虑了逼近一类拟变分包含问题解集与一族无限多个非扩张映象公共不动点集的某一公共元问题.在实Hilbert空间的框架下,证明了由次广义迭代算法产生的迭代序列强收敛到某一公共元.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.
-
Key words:
- variational inequality /
- fixed point /
- nonexpansive mapping /
- quasi-variational inclusion
-
[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.
计量
- 文章访问数: 1390
- HTML全文浏览量: 109
- PDF下载量: 733
- 被引次数: 0