Let C＇（α,β） be the class of functions f（z） =analytic in D ={z： ｜z｜ 〈 1}, satisfying for some convex function g（z） with g（O） = g＇（O） - 1 =- 0 and for allz in D the condition zf＇（z）-1/g（z）/zf＇（z...Let C＇（α,β） be the class of functions f（z） =analytic in D ={z： ｜z｜ 〈 1}, satisfying for some convex function g（z） with g（O） = g＇（O） - 1 =- 0 and for allz in D the condition zf＇（z）-1/g（z）/zf＇（z）/g（z）＋1-2α）｜ 〈β for some α β （0 ≤ α〈1,0 〈 β 〈 1）. A sharp coefficient estimate, distortion theorems and radius of convexity are determined for the class C＇（α ,β ）. The results extend the work of C. Selvaraj.展开更多
By introducing the notions of L-spaces and L_r-spaces, a complete generalization of Kalton's closed graph theorem is obtained. It points out the class of L_r-spaces is the maximal class of range spaces for the clo...By introducing the notions of L-spaces and L_r-spaces, a complete generalization of Kalton's closed graph theorem is obtained. It points out the class of L_r-spaces is the maximal class of range spaces for the closed graph theorem when the class of domain spaces is the class of Mackey spaces with weakly * sequentially complete dual.Some examples are constructed showing that the class of L_r-spaces is strictly larger than the class of separable B_r-complete spaces.Some properties of L-spaces and L_r-spaces are discussed and the relations between B-complete (resp. B_r-complete) spaces and L-spaces (resp. L_r-spaces) are given.展开更多
In this paper,we prove existence results of soutions for the nonlinear implicit complementarity problems NICP(T,S,K) where K is a closed weakly locally compact convex cone in a reflexive Banach space E,T is a nonlinea...In this paper,we prove existence results of soutions for the nonlinear implicit complementarity problems NICP(T,S,K) where K is a closed weakly locally compact convex cone in a reflexive Banach space E,T is a nonlinear operator from K into E* (i. e.,the dual space of E) and S is a nonlinear operator from K into E. Our results are the essential improvements and extension of the results obtained previously by several authors including Thera,Ding,and Zeng.展开更多
In this paper we prove three equivalent conditions of bounded closed convexset K in Banach space to have the drop and weak drop properties. We also give fourequivalent conditions of Banach space and its dual space to ...In this paper we prove three equivalent conditions of bounded closed convexset K in Banach space to have the drop and weak drop properties. We also give fourequivalent conditions of Banach space and its dual space to have the drop and weak dropproperties.展开更多
In this paper we study the connection between the metric projection operator PK ： B →K, where B is a reflexive Banach space with dual space B^＊ and K is a non-empty closed convex subset of B, and the generalized pr...In this paper we study the connection between the metric projection operator PK ： B →K, where B is a reflexive Banach space with dual space B^＊ and K is a non-empty closed convex subset of B, and the generalized projection operators ∏K ： B → K and πK ： B^＊ → K. We also present some results in non-reflexive Banach spaces.展开更多
文摘Let C＇（α,β） be the class of functions f（z） =analytic in D ={z： ｜z｜ 〈 1}, satisfying for some convex function g（z） with g（O） = g＇（O） - 1 =- 0 and for allz in D the condition zf＇（z）-1/g（z）/zf＇（z）/g（z）＋1-2α）｜ 〈β for some α β （0 ≤ α〈1,0 〈 β 〈 1）. A sharp coefficient estimate, distortion theorems and radius of convexity are determined for the class C＇（α ,β ）. The results extend the work of C. Selvaraj.
文摘By introducing the notions of L-spaces and L_r-spaces, a complete generalization of Kalton's closed graph theorem is obtained. It points out the class of L_r-spaces is the maximal class of range spaces for the closed graph theorem when the class of domain spaces is the class of Mackey spaces with weakly * sequentially complete dual.Some examples are constructed showing that the class of L_r-spaces is strictly larger than the class of separable B_r-complete spaces.Some properties of L-spaces and L_r-spaces are discussed and the relations between B-complete (resp. B_r-complete) spaces and L-spaces (resp. L_r-spaces) are given.
文摘In this paper,we prove existence results of soutions for the nonlinear implicit complementarity problems NICP(T,S,K) where K is a closed weakly locally compact convex cone in a reflexive Banach space E,T is a nonlinear operator from K into E* (i. e.,the dual space of E) and S is a nonlinear operator from K into E. Our results are the essential improvements and extension of the results obtained previously by several authors including Thera,Ding,and Zeng.
文摘In this paper we prove three equivalent conditions of bounded closed convexset K in Banach space to have the drop and weak drop properties. We also give fourequivalent conditions of Banach space and its dual space to have the drop and weak dropproperties.
文摘In this paper we study the connection between the metric projection operator PK ： B →K, where B is a reflexive Banach space with dual space B^＊ and K is a non-empty closed convex subset of B, and the generalized projection operators ∏K ： B → K and πK ： B^＊ → K. We also present some results in non-reflexive Banach spaces.
