一类广义集值变分包含组

A System of Generalized Set-valued Variational Inclusions

引入了一类新的广义集值变分包含组,应用预解算子技巧,建立了该类变分包含组与一类不动点问题的等价性,进而构造了求解该类变分包含组的迭代算法,并在适当的条件下,证明了该算法的收敛性.

A new system of generalized set-valued variational inclusions is introduced. By using the implicit resolvent operator technique, the equivalence of the new system of generalized set-valued variational inclusions with a class of fixed point problems is established, then the iterative algorithm for finding the approximate solutions of the system of generalized variational inclusions is proposed. Under suitable conditions, the convergence of the iterative sequence generated by the algorithm suggested is also given.