The auxiliary principle technique is extended to study a class of generalized set-valued strongly nonlinear mixed variational-like type inequalities. Firstly, the existence of solutions to the auxiliary problems for t...The auxiliary principle technique is extended to study a class of generalized set-valued strongly nonlinear mixed variational-like type inequalities. Firstly, the existence of solutions to the auxiliary problems for this class of generalized set-valued strongly nonlinear mixed variational-like type inequalities is shown. Secondly, the iterative algorithm for solving this class of generalized set-valued strongly nonlinear mixed variational-like type inequalities is given by using this existence result. Finally, the strong convergence of iterative sequences generated by the algorithm is proven. The present results improve, generalize and modify the earlier and recent ones obtained previously by some authors in the literature.展开更多
This paper deals with Henig globally efficiency in vector optimization involving generalized cone-preinvex set-valued mapping. Some properties of generalized cone-preinvex set-valued map are derived. It also disclose ...This paper deals with Henig globally efficiency in vector optimization involving generalized cone-preinvex set-valued mapping. Some properties of generalized cone-preinvex set-valued map are derived. It also disclose the closed relationships between Henig globally efficiency of generalized conepreinvex set-valued optimization problem and Henig globally efficiency of a kind of vector variational inequality.展开更多
Under new assumptions,this paper obtains some extended versions of Ky Fan type inequality for a family of C-continuous set-valued mappings in the setting of topological semilattices.The obtained results are new and di...Under new assumptions,this paper obtains some extended versions of Ky Fan type inequality for a family of C-continuous set-valued mappings in the setting of topological semilattices.The obtained results are new and different from the corresponding known results in the literature.Some special cases of the main result are also discussed.Some examples are given to illustrate the results.展开更多
基金the Teaching and Research Award Fund for Outstanding Young Teachers in Higher Education Institutions of MOE,Chinathe Dawn Program Foundationin Shanghai
文摘The auxiliary principle technique is extended to study a class of generalized set-valued strongly nonlinear mixed variational-like type inequalities. Firstly, the existence of solutions to the auxiliary problems for this class of generalized set-valued strongly nonlinear mixed variational-like type inequalities is shown. Secondly, the iterative algorithm for solving this class of generalized set-valued strongly nonlinear mixed variational-like type inequalities is given by using this existence result. Finally, the strong convergence of iterative sequences generated by the algorithm is proven. The present results improve, generalize and modify the earlier and recent ones obtained previously by some authors in the literature.
基金supported by the Natural Science Foundation of China under Grant No.11361001Ministry of Education Science and technology key projects under Grant No.212204+1 种基金the Natural Science Foundation of Ningxia under Grant No.NZ12207the Science and Technology key project of Ningxia institutions of higher learning under Grant No.NGY2012092
文摘This paper deals with Henig globally efficiency in vector optimization involving generalized cone-preinvex set-valued mapping. Some properties of generalized cone-preinvex set-valued map are derived. It also disclose the closed relationships between Henig globally efficiency of generalized conepreinvex set-valued optimization problem and Henig globally efficiency of a kind of vector variational inequality.
基金partially supported by NAFOSTED under Grant No.101.01-2014.17UTC under Grant No.T2017-KHCB-60
文摘Under new assumptions,this paper obtains some extended versions of Ky Fan type inequality for a family of C-continuous set-valued mappings in the setting of topological semilattices.The obtained results are new and different from the corresponding known results in the literature.Some special cases of the main result are also discussed.Some examples are given to illustrate the results.
