一类新的广义非线性变分不等式系统的预解算子算法

Resolvent Operator Algorithm for a Class of New System of General Nonlinear Variational Inequalities

考虑Hilbert空间中一类新的广义非线性变分不等式系统(SGNLVI),建立了SGNLVI和不动点问题之间的等价性;并利用预解算子方法,对(SGNLVI)问题提出一个新的预解算子算法,在适当的条件下分析了该算法的收敛性;给出的结果是更一般的结果,这些结果改进并推广了相关文献中的结论.

This paper introduces and studies a new system of general nonlinear variational inequalities （SGNLVI） in Hilbert space.The equivalence between （SGNLVI） and the fixed point problems is established.Using the resolvent operator technique, this paper presents a new resolvent algorithm and the convergence of the new algorithm is analyzed under proper conditions.The results presented in this paper are more general to improve and extend the results known in the previous literature.