关于一类新的完备广义强非线性隐拟变分不等式

ON A NEW CLASS OF COMPLETELY GENERALIZEDSTRONGLY NONLINEAR IMPLICIT QUASIVARIATIONAL INEQUALITIES

研究一类新的完备广义强非线性隐拟变分不等式问题：ＣＧＳＮＩＱＶＩＰ（Ｎ（，），Ｆ，Ｇ，Ｍ，ｇ，Ｋ（ｚ））．证明了解这类变分不等式与解某个不动点问题之间的等价关系．用这种等价关系，提出了求完备广义强非线性隐拟变分不等式的逼近解的迭代算法．在无紧性条件下证明了由算法生成的迭代序列的收敛性和ＣＧＳＮＩＱＶＩＰ（Ｎ（，），Ｆ，Ｇ，Ｍ，ｇ，Ｋ（ｘ））的解的存在性．

This paper introduces and studies a new class of completely generalized strongly nonlinear implicit quasivariational inequality problems:CGSNIQVIP((N·,·),F,G,M,g,K(x)).It is proved that a completely generalized strong nonlinear implicit quasivariational inequality problem is equivalent to solving a fixed point problem. By using the equivalence, a iterative algorithm for finding the approximate solutons of the completely generalized strong nonlinear implicit quasivariational inequality problem is suggested and analyzed. The convergence criteria for the algorithm and the existnece of solutions for the CGSNIQVIP(N(·,·),F,G,M,g,K(x)) are also disscussed without compacteness. These new results include many known results for variational inequalities and complementarity problems as special cases.