In this paper,we prove that a proper μ holomorphic mapping f:D 1→D 2 between bounded domains with some convexity,such that f satisfies some growth condition,extends smoothly to bD 1-{z:U(z)=0}.
A kind of tangent derivative and the concepts of strong and weak * pseudoconvexity for a set-valued map are introduced. By the standard separation theorems of the convex sets and cones the optimality Fritz John condit...A kind of tangent derivative and the concepts of strong and weak * pseudoconvexity for a set-valued map are introduced. By the standard separation theorems of the convex sets and cones the optimality Fritz John condition of set-valued optimization under Benson proper efficiency is established, its sufficience is discussed. The form of the optimality conditions obtained here completely tally with the classical results when the set-valued map is specialized to be a single-valued map.展开更多
Several equivalent statements of generalized subconvexlike set-valued map are established in ordered linear spaces. Using vector closure, we introduce Benson proper efficient solution of vector optimization problem. U...Several equivalent statements of generalized subconvexlike set-valued map are established in ordered linear spaces. Using vector closure, we introduce Benson proper efficient solution of vector optimization problem. Under the assumption of generalized subconvexlikeness, scalarization, multiplier and saddle point theorems are obtained in the sense of Benson proper efficiency.展开更多
E E. Browder and W. V. Petryshyn defined the topological degree for A- proper mappings and then W. V. Petryshyn studied a class of A-proper mappings, namely, P1-compact mappings and obtained a number of important fixe...E E. Browder and W. V. Petryshyn defined the topological degree for A- proper mappings and then W. V. Petryshyn studied a class of A-proper mappings, namely, P1-compact mappings and obtained a number of important fixed point theorems by virtue of the topological degree theory. In this paper, following W. V. Petryshyn, we continue to study P1-compact mappings and investigate the boundary condition, under which many new fixed point theorems of P1-compact mappings are obtained. On the other hand, this class of A-proper mappings with the boundedness property includes completely continuous operators and so, certain interesting new fixed point theorems for completely continuous operators are obtained immediately. As a result of it, our results generalize several famous theorems such as Leray-Schauder＇s theorem, Rothe＇s theorem, Altman＇s theorem, Petryshyn＇s theorem, etc.展开更多
Under the assumption that the ordering cone has a nonempty interior and is separable （or the feasible set has a nonempty interior and is separable）, we give scalarization theorems on Benson proper effciency. Applyin...Under the assumption that the ordering cone has a nonempty interior and is separable （or the feasible set has a nonempty interior and is separable）, we give scalarization theorems on Benson proper effciency. Applying the results to vector optimization problems with nearly cone-subconvexlike set-valued maps, we obtain scalarization theorems and Lagrange multiplier theorems for Benson proper effcient solutions.展开更多
Let G be a generalized matrix algebra over a commutative ring R and Z（G） be the center of G. Suppose that F, T ：G→G are two co-commuting R-linear mappings, i.e., F（x）x = xT（x） for all x ∈ G. In this note, we ...Let G be a generalized matrix algebra over a commutative ring R and Z（G） be the center of G. Suppose that F, T ：G→G are two co-commuting R-linear mappings, i.e., F（x）x = xT（x） for all x ∈ G. In this note, we study the question of when co-commuting mappings on G are proper.展开更多
It is proved that every proper holomorphic self-mapping of some kinds of Generalized Hartogs Triangles is an automorphism.and its explicit expression is given.
文摘In this paper,we prove that a proper μ holomorphic mapping f:D 1→D 2 between bounded domains with some convexity,such that f satisfies some growth condition,extends smoothly to bD 1-{z:U(z)=0}.
文摘A kind of tangent derivative and the concepts of strong and weak * pseudoconvexity for a set-valued map are introduced. By the standard separation theorems of the convex sets and cones the optimality Fritz John condition of set-valued optimization under Benson proper efficiency is established, its sufficience is discussed. The form of the optimality conditions obtained here completely tally with the classical results when the set-valued map is specialized to be a single-valued map.
文摘Several equivalent statements of generalized subconvexlike set-valued map are established in ordered linear spaces. Using vector closure, we introduce Benson proper efficient solution of vector optimization problem. Under the assumption of generalized subconvexlikeness, scalarization, multiplier and saddle point theorems are obtained in the sense of Benson proper efficiency.
基金Supported in part by Education Ministry,Anhui Province,China(No:2003kj047zd)
文摘E E. Browder and W. V. Petryshyn defined the topological degree for A- proper mappings and then W. V. Petryshyn studied a class of A-proper mappings, namely, P1-compact mappings and obtained a number of important fixed point theorems by virtue of the topological degree theory. In this paper, following W. V. Petryshyn, we continue to study P1-compact mappings and investigate the boundary condition, under which many new fixed point theorems of P1-compact mappings are obtained. On the other hand, this class of A-proper mappings with the boundedness property includes completely continuous operators and so, certain interesting new fixed point theorems for completely continuous operators are obtained immediately. As a result of it, our results generalize several famous theorems such as Leray-Schauder＇s theorem, Rothe＇s theorem, Altman＇s theorem, Petryshyn＇s theorem, etc.
基金Supported by the National Natural Science Foundation of China (10571035,10871141)
文摘Under the assumption that the ordering cone has a nonempty interior and is separable （or the feasible set has a nonempty interior and is separable）, we give scalarization theorems on Benson proper effciency. Applying the results to vector optimization problems with nearly cone-subconvexlike set-valued maps, we obtain scalarization theorems and Lagrange multiplier theorems for Benson proper effcient solutions.
文摘Let G be a generalized matrix algebra over a commutative ring R and Z（G） be the center of G. Suppose that F, T ：G→G are two co-commuting R-linear mappings, i.e., F（x）x = xT（x） for all x ∈ G. In this note, we study the question of when co-commuting mappings on G are proper.
基金Project supported by the National Natural Science Foundation of China(No.19631010)
文摘It is proved that every proper holomorphic self-mapping of some kinds of Generalized Hartogs Triangles is an automorphism.and its explicit expression is given.
