The multivalued general mixed implicit equilibrium-like problems are introduced and studied. To solve these problems, a new predictor-corrector iterative algorithm is proposed and analyzed using the auxiliary principl...The multivalued general mixed implicit equilibrium-like problems are introduced and studied. To solve these problems, a new predictor-corrector iterative algorithm is proposed and analyzed using the auxiliary principle technique. The convergence of the suggested algorithm is also proved in weaker conditions.展开更多
A new system of generalized mixed implicit equilibrium problems is introduced and studied in Banach spaces. First, the notion of the Yosida proximal mapping for generalized mixed implicit equilibrium problems is intro...A new system of generalized mixed implicit equilibrium problems is introduced and studied in Banach spaces. First, the notion of the Yosida proximal mapping for generalized mixed implicit equilibrium problems is introduced. By using the notion, a system of generalized equation problems is considered, and its equivalence with the system of generalized mixed implicit equilibrium problems is also proved. Next, by applying the system of generalized equation problems, we suggest and analyze an iterative algorithm to compute the approximate solutions of the system of generalized mixed implicit equilibrium problems. The strong convergence of the iterative sequences generated by the algorithm is proved under quite mild conditions. The results are new and unify and generalize some recent results in this field.展开更多
A new class of generalized mixed implicit quasi-equilibrium problems （GMIQEP） with four-functions is introduced and studied. The new class of equilibrium problems includes many known generalized equilibrium problems...A new class of generalized mixed implicit quasi-equilibrium problems （GMIQEP） with four-functions is introduced and studied. The new class of equilibrium problems includes many known generalized equilibrium problems and generalized mixed implicit quasi-variational inequality problems as many special cases. By employing the auxiliary principle technique, some predictor-corrector iterative algorithms for solving the GMIQEP are suggested and analyzed. The convergence of the suggested algorithm only requires the continuity and the partially relaxed implicit strong monotonicity of the mappings展开更多
A new system of generalized mixed implicit equilibrium problems （SGMIEP） involving nonmonotone set-valued mappings is introduced and studied in real reflexive Banach spaces. First, an auxiliary mixed equilibrium pro...A new system of generalized mixed implicit equilibrium problems （SGMIEP） involving nonmonotone set-valued mappings is introduced and studied in real reflexive Banach spaces. First, an auxiliary mixed equilibrium problem （AMEP） is introduced. The existence and the uniqueness of the solutions to the AMEP are proved under quite mild assumptions without any coercive conditions. Next, by using the solution mapping of the AMEP, a system of generalized equation problems （SGEP） is considered, and its equivalence with the SGMIEP is shown. By using the SGEP, a new iterative algorithm for solving the SGMIEP is proposed and analyzed. The strong convergence of the iterative sequences generated by the algorithm is proved under suitable conditions. These results are new, which unify and generalize some recent results in this field.展开更多
基金Project supported by the National Natural Science Foundation of China(No.10771173)
文摘The multivalued general mixed implicit equilibrium-like problems are introduced and studied. To solve these problems, a new predictor-corrector iterative algorithm is proposed and analyzed using the auxiliary principle technique. The convergence of the suggested algorithm is also proved in weaker conditions.
基金Project supported by the Scientific Research Fund of Sichuan Normal University(No.09ZDL04)the Sichuan Province Leading Academic Discipline Project(No.SZD0406)
文摘A new system of generalized mixed implicit equilibrium problems is introduced and studied in Banach spaces. First, the notion of the Yosida proximal mapping for generalized mixed implicit equilibrium problems is introduced. By using the notion, a system of generalized equation problems is considered, and its equivalence with the system of generalized mixed implicit equilibrium problems is also proved. Next, by applying the system of generalized equation problems, we suggest and analyze an iterative algorithm to compute the approximate solutions of the system of generalized mixed implicit equilibrium problems. The strong convergence of the iterative sequences generated by the algorithm is proved under quite mild conditions. The results are new and unify and generalize some recent results in this field.
基金Project supported by the Natural Science Foundation of Sichuan Educational Commission (No.2003A081)
文摘A new class of generalized mixed implicit quasi-equilibrium problems （GMIQEP） with four-functions is introduced and studied. The new class of equilibrium problems includes many known generalized equilibrium problems and generalized mixed implicit quasi-variational inequality problems as many special cases. By employing the auxiliary principle technique, some predictor-corrector iterative algorithms for solving the GMIQEP are suggested and analyzed. The convergence of the suggested algorithm only requires the continuity and the partially relaxed implicit strong monotonicity of the mappings
基金Project supported by the Sichuan Province Leading Academic Discipline Project(No.SZD0406)the Scientific Research Fund of Sichuan Normal University(No.11ZDL01)
文摘A new system of generalized mixed implicit equilibrium problems （SGMIEP） involving nonmonotone set-valued mappings is introduced and studied in real reflexive Banach spaces. First, an auxiliary mixed equilibrium problem （AMEP） is introduced. The existence and the uniqueness of the solutions to the AMEP are proved under quite mild assumptions without any coercive conditions. Next, by using the solution mapping of the AMEP, a system of generalized equation problems （SGEP） is considered, and its equivalence with the SGMIEP is shown. By using the SGEP, a new iterative algorithm for solving the SGMIEP is proposed and analyzed. The strong convergence of the iterative sequences generated by the algorithm is proved under suitable conditions. These results are new, which unify and generalize some recent results in this field.
