Strong convergence theorem of common elements for variational inequality solution set and the set of common fixed point for a finite family of semi-contractive mappings(变分不等式解集和半压缩映射有限族公共不动点集的公共元的强收敛定理)

Abstract

An inertial viscous iterative algorithm is constructed for the common elements of variational inequality problems and fixed point problems. Under appropriate assumptions, it is proved that the iterative sequence generated by the constructed algorithm strongly converges to the common elements of the solution set of pseudo-monotone variational inequalities and the common fixed point set of a finite family of semi-contractive mappings by using demi-closed at zero,projection operator and other analysis techniques. Numerical experiments illustrate the effectiveness of the algorithm. The study of this paper improves and extends some recent relative results.(在Hilbert空间中，针对变分不等式问题和不动点问题的公共元，构造了一种惯性黏性迭代算法。在适当条件下，采用映射半闭定义和投影算子技巧，证明了所构造算法产生的迭代序列强收敛于伪单调变分不等式解集和半压缩映射有限族公共不动点集的公共元。数值实验结果说明了该算法的有效性。所得结果改进和推广了已有文献的一些结果。)

Keywords

• variational inequalities(变分不等式)
• fixed points(不动点)
• a finite family of semi-contractive mappings(半压缩映射有限族)
• strong convergence(强收敛性)