引入了一类新的关于松驰协强制映射的广义变分不等式组,通过用度量投影的方法证明了这类广义变分不等式组解的存在性和唯一性,而且建立了一类新的算法来逼近这一不等式组的解,同时讨论了该算法的收敛性,使得近期相关结果成为所得结果的特殊情况.
[1] Chang SS, Lee HWJ, Chan CK. Generalized system for relaxed cocoercive variational inequalities in Hilbert spaces [J]. Applied mathematics letters 2007, 3(3).
[2] Muhammad Aslam Noor. General variational inequalities and nonexpansive mappings [J]. Journal of Mathematical Analysis and Applications 2007, 2(2).
[3] Verma RU. General convergence analysis for two-step projection methods and applications to variational problems [J]. Applied mathematics letters 2005, 11(11).
[4] NIE H, LIU Z, KIM K H. A system of nonlinear variational inequalitiesinvolving strongly monotone and pseudocontractive mappings [J]. Adv Nonlinear Var Inequal 2003, 6(02).
[5] R. U. Verma. Generalized System for Relaxed Cocoercive Variational Inequalities and Projection Methods [J]. Journal of Optimization Theory and Applications 2004, 1(1).
[6] FANG Yaping, HUANG Nanjing. A new system of variational inclusions with (H, η)-monotoneoperators in Hilbert spaces [J]. Computers & Mathematics with Applications 2005, 49.