变分不等式问题和半压缩映射有限簇的强收敛定理  

Strong Convergence Theorem of Variational Inequality Problems and a Finite Family of Semi-contractive Mappings

作　　者：房萌凯 高兴慧[1] 郭玥蓉 王永杰 FANG Mengkai;GAO Xinghui;GUO Yuerong;WNAG Yongjie(School of Mathematics and Computer Science,Yan’an University,Yan’an 716099,China)

机构地区：[1]延安大学数学与计算机科学学院,陕西延安716099

出　　处：《贵州大学学报（自然科学版）》2024年第1期31-36,共6页Journal of Guizhou University:Natural Sciences

基　　金：国家自然科学基金资助项目(61866038);国家级大学生创新训练计划资助项目(202210719022);延安大学研究生教育创新计划资助项目(YCX2023012)。

摘　　要：在Hilbert空间中,首先,构造了一种新的平行迭代方法用于逼近伪单调变分不等式的解集和半压缩映射有限簇的公共不动点集的公共元;其次,在适当假设条件下,证明了该算法生成的迭代序列的强收敛性;最后,给出具体的数值实验检验了所提出算法的有效性。In Hilbert spaces,firstly,a new parallel iterative method is proposed to approximate the common elements of the set of solutions of pseudo-monotone variational inequality and a common fixed point set of a finite family of semi-contractive mappings.Secondly,under appropriate assumptions,the strong convergence of the iterative sequence generated by this algorithm is proved.Finally,some concrete numerical experiments are also included to explain the effectiveness of the proposed methods.

关 键 词：变分不等式 半压缩映射有限簇 强收敛定理 

分 类 号：O177.91[理学—数学]