关于一类一般集值混合似变分不等式与η-广义集值内隐豫解方程

On a Class of General Mixed Variational like Inequalities and η Generalized Set Valued Implicit Resolvent Equations

研究一类新的一般集值混合似变分不等式问题：ＧＳＭＬＶＩＰ（ Ｎ，Ｔ，Ｖ，Ｇ，ｇ，η，φ） ．在Ｄｉｎｇ 和Ｌｏｕ（Ｊ．Ｃｏｍｐｕｔ．Ａｐｐｌ．Ｍａｔｈ．，ｉｎ ｐｒｉｎｔ．） 提出η近似映象等概念基础上，引入了η广义集值内隐豫解方程的概念．证明了一般集值混合似变分不等式与η广义集值内隐豫解方程之间的等价性．利用这种等价关系，提出了一种求一般集值混合似变分不等式解的迭代算法．该算法的收敛性也被讨论和分析．这些结果包含了该领域许多结果作为特殊情形．

This paper introduces and studies a new class of general set valued mixed variational like inequality problem: GSMLVIP(N,T,V,G,g,η,φ). By using the concept of η proximal mapping due to Ding and Lou(J. Comput. Appl. Math.,in print.), the concept of η generalized set valued implicit resolvent equations is introduced. The equivalence between general set valuedmixed variational like inequality and η generalized set valued implicit resolvent equation is shown. By using the equivalence, a iterative algorithm for finding the approximate solutions of the general set valued mixed variational like inequality problems are suggested. The convergence criteria for the algorithm is also discussed and analyzed. These new results include many known resulets in the field as special cases.