| In this paper, we mainly study the applications of resolvent operator technique to the iterative algorithms of some generalized set-valued variational inclusions and some systems of generalized set-valued variational inclusions and prove the strongly convergence of the iterative sequence generated by the given algorithms in Hilbert space. At same time, we establish systems of coincidence theorem and system of minimax theorems in G-convex under weaker assumptions. Our results generalize the corresponding results in recent literature. The first, we introduce the maximal η-monotone mapping and -monotone operator, define a new class of monotone mappings——g-η-monotone mapping, study the property of g -η-monotone mapping, introduce the resolvent operator produced by h-monotone mapping and define the resolvent operator produced by the g -η-monotone mapping. The second, by using the resolvent operator technique associated with h-monotone operator, an iterative algorithm for generalized set-valued variational inclusion is suggested and analyzed. The convergence of iterative sequence generated by the algorithm is proved. At the same time, by using the resolvent operator technique associated with a new class of monotone mappings——g -η-monotone mapping, An iterative algorithm for approximating the solutions of generalized implicit variational-like inclusion is suggested and analyzed. The convergence of iterative sequence generated by the algorithm is also proved. Thirdly, by using the η?maximal monotone mapping, an iterative algorithm to compute the approximate solution of systems of generalized quasi-variational-like inclusions is suggested and analyzed. The convergence of iterative sequences generated by the algorithm is also proved. At last, we establish systems of coincidence theorem and system of minimax theorems in G-convex under weaker assumptions. Our results generalize the corresponding results in recent literature. |
