广义集值强非线性混合似变分不等式的辅助原理和三步迭代算法

使用辅助原理技巧研究了一类广义集值强非线性混合变分不等式．证明了此类集值强非线性混合变分不等式辅助问题解的存在性和唯一性;构建了一个新的三步迭代算法,通过辅助原理技巧,构建并计算此类非线性混合变分不等式的近似解,进一步证明非线性混合变分不等式解的存在性以及由算法产生的三个序列的收敛性．所得结论推广了近年来许多混合变分不等式和准变分不等式以及他们的有关结果．

Auxiliary Principle and Three-Step Iterative Algorithms for Generalized Set-Valued Strongly Nonlinear Mixed Variational-Like Inequalities

The auxiliary principle technique to study a class of generalized setvalued strongly nonlinear mixed variational-like inequalities is extended.The existence and uniqueness of the solution of the auxiliary problem for the generalized set-valued strongly nonlinear mixed variational-like inequalities was proved.A novel and innovative three-step iterative algorithm to compute approximate solution was constructed.And the existence of the solution of the generalized set-valued strongly nonlinear mixed variational-like inequality was showed by using the auxiliary principle technique.The convergence of three-step iterative sequences generated by the algorithm was also proved.