Hilbert空间中一般形式的松弛余强制变分不等方程组解的迭代逼近问题

Iterative approximation of solutions of generalized system for relaxed cocoercive variational inequalities in hilbert spaces

引入和研究了一般形式的松弛余强制变分不等方程组解的迭代逼近问题:求x1*,x2*,…,x*N∈K,使得〈ρ1T(x2*,x1*)+x1*-x2*,y-x1*〉≥0,y∈K,〈ρ2T(x3*,x2*)+x2*-x3*,y-x2*〉≥0,y∈K,┇〈ρN-1T(x*N,x*N-1)+x*N-1-x*N,y-xN*-1〉≥0,y∈K,其中N≥2是一正整数,ρ,ρ,…,ρ≥0是给定的常数.改进和推广了已知的相应结果.

The author introduces and studies the following approximate solvability problem of generalized system for relaxed cocoercive variational inequalities in Hilbert spaces： {〈ρ1T（x2^＊,x1^＊）＋x1^＊-x2^＊,y-x1^＊〉≥0,arbitary y∈K,〈ρ2T（x3^＊,x2^＊）＋x2^＊-x3^＊,y-x2^＊〉≥0,arbitary y∈K,…〈ρN-1T（xN^＊,xN-1^＊）＋xN-1^＊-xN^＊,y-xN-1^＊〉≥0,arbitary y∈K. The results presented in the paper generalize and improve the corresponding results.