STRONG CONVERGENCE THEOREMS FOR ASYMPTOTICALLY QUASI-NONEXPANSIVE MAPPINGS AND INVERSE-STRONGLY MONOTONE MAPPINGS
作者： Yong-Chun Xu , Zhen He , Xin-Feng He
DOI: 10.7858/EAMJ.2011.27.1.001
关键词: Strongly monotone 、 Projection (mathematics) 、 Discrete mathematics 、 Real number 、 Mathematics 、 Sequence 、 Monotone polygon 、 Hilbert space 、 Variational inequality 、 Regular polygon
摘要: Abstract. In this paper, we consider an iterative scheme for ndinga common element of the set xed points a asymptotically quasi-nonexpansive mapping and solutions variational inequal-ity inverse strongly monotone in Hilbert space. Thenwe show that sequence converges to oftwo sets. Using result, problem nding com-mon point astrictly pseudocontractive commonelement quasi-nonexpansivemapping zeros inverse-strongly mapping. 1. Introduction preliminariesLet Cbe closed convex subset real space Hand let P C be themetric projection Honto C.A Aof Cinto His called if all x;y2C,hx y;AxAyi0:The inequality is nd u2Csuch hv u;Aui0 v2C; see [1,2,4,6,11]. The inequalityis denoted by VI(C;A).A there existsa positive number such hx y;Ax Ayi kAx Ayk
koreascience.or.kr参考文章(13)
Fengshan Liu, M. Zuhair Nashed, Regularization of Nonlinear Ill-Posed Variational Inequalities and Convergence Rates Set-valued Analysis. ,vol. 6, pp. 313- 344 ,(1998) , 10.1023/A:1008643727926
K. Goebel, W. A. Kirk, A FIXED POINT THEOREM FOR ASYMPTOTICALLY NONEXPANSIVE MAPPINGS Proceedings of the American Mathematical Society. ,vol. 35, pp. 171- 174 ,(1972) , 10.1090/S0002-9939-1972-0298500-3
W. Takahashi, Nonlinear complementarity problem and systems of convex inequalities Journal of Optimization Theory and Applications. ,vol. 24, pp. 499- 506 ,(1978) , 10.1007/BF00932892
Jong Kyu Kim, Young Man Nam, Jae Yull Sim, Convergence theorems of implicit iterative sequences for a finite family of asymptotically quasi-nonexpansive type mappings Nonlinear Analysis: Theory, Methods & Applications. ,vol. 71, pp. e2839- e2848 ,(2009) , 10.1016/J.NA.2009.06.090
Tae-Hwa Kim, Hong-Kun Xu, Strong convergence of modified Mann iterations for asymptotically nonexpansive mappings and semigroups Nonlinear Analysis-theory Methods & Applications. ,vol. 64, pp. 1140- 1152 ,(2006) , 10.1016/J.NA.2005.05.059
Felix E. Browder, Nonlinear monotone operators and convex sets in Banach spaces Bulletin of the American Mathematical Society. ,vol. 71, pp. 780- 785 ,(1965) , 10.1090/S0002-9904-1965-11391-X
Felix E. Browder, The Fixed Point Theory of Multi-valued Mappings in Topological Vector Spaces. Mathematische Annalen. ,vol. 177, pp. 283- 301 ,(1968) , 10.1007/BF01350721
Hideaki Iiduka, Wataru Takahashi, Strong convergence theorems for nonexpansive mappings and inverse-strongly monotone mappings Nonlinear Analysis-theory Methods & Applications. ,vol. 61, pp. 341- 350 ,(2005) , 10.1016/J.NA.2003.07.023
F.E Browder, W.V Petryshyn, Construction of fixed points of nonlinear mappings in Hilbert space Journal of Mathematical Analysis and Applications. ,vol. 20, pp. 197- 228 ,(1967) , 10.1016/0022-247X(67)90085-6
Ronald E Bruck, On the weak convergence of an ergodic iteration for the solution of variational inequalities for monotone operators in Hilbert space Journal of Mathematical Analysis and Applications. ,vol. 61, pp. 159- 164 ,(1977) , 10.1016/0022-247X(77)90152-4