Hilbert空间中关于不动点问题,变分不等式系统和分裂均衡问题迭代算法的强收敛定理  

The Strong Convergence Theorem of Iterative Algorithms for the Fixed Point Problem,a System of Variational Inequalities,and a Split Equilibrium Problem in Hilbert Spaces

作　　者：潘灵荣 王元恒 Pan Lingrong;Wang Yuanheng(Wenling Institute,Zhejiang Open University,Zhejiang Wenling 317500;College of Mathematics and Computer Science,Zhejiang Normal University,Zhejiang Jinhua 321004)

机构地区：[1]浙江开放大学温岭学院,浙江温岭317500 [2]浙江师范大学数学与计算机科学学院,浙江金华321004

出　　处：《数学物理学报（A辑）》2023年第6期1880-1896,共17页Acta Mathematica Scientia

基　　金：国家自然科学基金(12171435);浙江省教育厅科研项目(Y202146280)。

摘　　要：在Hilbert空间中,考虑渐近非扩张映像的不动点问题,变分不等式系统和分裂均衡问题的一个公共解.在适当的参数限制条件下,证明了所构造的修正粘性迭代序列强收敛到以上三类问题的一个公共元,所得结论改进和推广了一些最近文献的相关结果.In this paper,we consider a common solution of three problems in real Hilbert spaces including the fixed points problem for asymptotically nonexpansive mapping,a system of variational inequalities and the split equilibrium problem.Under some suitable conditions imposed on the sequence of parameters,we prove that the sequence generated by the modified viscosity approximation method converges strongly to a common element of the solution set of these three kinds of problems.The results obtained in this article extend and improve the corresponding results of the relevant literature.

关 键 词：渐近非扩张映像 变分不等式系统 分裂均衡问题 不动点问题 

分 类 号：O177.911[理学—数学]