Firstly, in the general normed linear space, the concepts of generalized isosceles orthogonal group, generalized Birkhoff orthogonal group, generalized Roberts orthogonal group, strong Birkhoff orthogonal group and ge...Firstly, in the general normed linear space, the concepts of generalized isosceles orthogonal group, generalized Birkhoff orthogonal group, generalized Roberts orthogonal group, strong Birkhoff orthogonal group and generalized orthogonal basis are introduced. Secondly, the conclusion that any two nonzero generalized orthogonal groups must be linearly independent group is proven. And the existence of nonzero generalized orthogonal group and its linear correlation are discussed preliminarily, as well as some related properties of nonempty generalized orthogonal group in specific normed linear space namely the <em>l<sub>p</sub></em> space.展开更多
Some results from the theory of best (or best simultaneous) approximation in a narmed linear space have been extended to a normed almost linear space [strong normed almost linear space].
Since the PN space (E, F) which satisfies condition (PN-5) is just a Menger PN-space (E, F, min), the results with regard to probabilistic norms of linear operators on PN-spaces obtained by Xiao Jianzhong have bigger ...Since the PN space (E, F) which satisfies condition (PN-5) is just a Menger PN-space (E, F, min), the results with regard to probabilistic norms of linear operators on PN-spaces obtained by Xiao Jianzhong have bigger limitations. In this paper, problems respecting probabilistic norms of linear operators and spaces of operators are studied on more general Menger PN-spaces. The results presented improve and generalize the corresponding results by Xiao.展开更多
In [1],a family of angles are defined in normed linear spaces. In this paper,it is shown that if anyone of the angles satisfies certain euclidean triangle congruence properties,the space must be an inner product space.
In this paper, we discuss the average errors of function approximation by linear combinations of Bernstein operators. The strongly asymptotic orders for the average errors of the combinations of Bernstein operators se...In this paper, we discuss the average errors of function approximation by linear combinations of Bernstein operators. The strongly asymptotic orders for the average errors of the combinations of Bernstein operators sequence are determined on the Wiener space.展开更多
Ishikawa iterative sequences with errors different from the iterative sequences introduced by Liu and Xu are given. Moreover, the problem of approximating the fixed points of （ψ）-hemicontractive mapping in normed l...Ishikawa iterative sequences with errors different from the iterative sequences introduced by Liu and Xu are given. Moreover, the problem of approximating the fixed points of （ψ）-hemicontractive mapping in normed linear spaces by the modified Ishikawa iterative sequences with errors is investigated. The results presented in this paper improve and extend the results of the others.展开更多
In general normed spaces, we consider a multiobjective piecewise linear optimization problem with the ordering cone being convex and having a nonempty interior. We establish that the weak Pareto optimal solution set o...In general normed spaces, we consider a multiobjective piecewise linear optimization problem with the ordering cone being convex and having a nonempty interior. We establish that the weak Pareto optimal solution set of such a problem is the union of finitely many polyhedra and that this set is also arcwise connected under the cone convexity assumption of the objective function. Moreover, we provide necessary and sufficient conditions about the existence of weak (sharp) Pareto solutions.展开更多
The problem whether every infinite dimensional Banach space has an infinite dimensional separable quotient space has remained unsolved for a long time. In this paper we prove: the Banach space X has an infinite dimens...The problem whether every infinite dimensional Banach space has an infinite dimensional separable quotient space has remained unsolved for a long time. In this paper we prove: the Banach space X has an infinite dimensional separable quotient if and only if X has an infinite dimensional separable quasicomplemented subspace, also if and only if there exists a Banach space Y and a bounded linear operator T is an element of B(Y,X such that the range of T is nonclosed and dense in X. Besides, the other relevant questions for such spaces e.g. the question on operator ideals that on H.I.(hereditarily indecomposable) spaces, that on invariant subspaces of operators, etc, are also discussed.展开更多
Assume X is a normed space,every x ＊ ∈ S（X＊） can reach its norm at some point in B（X）,and Y is a β-normed space.If there is a quotient space of Y which is asymptotically isometric to l β,then L（X,Y） contain...Assume X is a normed space,every x ＊ ∈ S（X＊） can reach its norm at some point in B（X）,and Y is a β-normed space.If there is a quotient space of Y which is asymptotically isometric to l β,then L（X,Y） contains an asymptotically isometric copy of l β.Some sufficient conditions are given under which L（X,Y） fails to have the fixed point property for nonexpansive mappings on closed bounded β-convex subsets of L（X,Y）.展开更多
文摘Firstly, in the general normed linear space, the concepts of generalized isosceles orthogonal group, generalized Birkhoff orthogonal group, generalized Roberts orthogonal group, strong Birkhoff orthogonal group and generalized orthogonal basis are introduced. Secondly, the conclusion that any two nonzero generalized orthogonal groups must be linearly independent group is proven. And the existence of nonzero generalized orthogonal group and its linear correlation are discussed preliminarily, as well as some related properties of nonempty generalized orthogonal group in specific normed linear space namely the <em>l<sub>p</sub></em> space.
文摘Some results from the theory of best (or best simultaneous) approximation in a narmed linear space have been extended to a normed almost linear space [strong normed almost linear space].
文摘Since the PN space (E, F) which satisfies condition (PN-5) is just a Menger PN-space (E, F, min), the results with regard to probabilistic norms of linear operators on PN-spaces obtained by Xiao Jianzhong have bigger limitations. In this paper, problems respecting probabilistic norms of linear operators and spaces of operators are studied on more general Menger PN-spaces. The results presented improve and generalize the corresponding results by Xiao.
文摘In [1],a family of angles are defined in normed linear spaces. In this paper,it is shown that if anyone of the angles satisfies certain euclidean triangle congruence properties,the space must be an inner product space.
文摘In this paper, we discuss the average errors of function approximation by linear combinations of Bernstein operators. The strongly asymptotic orders for the average errors of the combinations of Bernstein operators sequence are determined on the Wiener space.
文摘Ishikawa iterative sequences with errors different from the iterative sequences introduced by Liu and Xu are given. Moreover, the problem of approximating the fixed points of （ψ）-hemicontractive mapping in normed linear spaces by the modified Ishikawa iterative sequences with errors is investigated. The results presented in this paper improve and extend the results of the others.
基金supported by the National Natural Science Foundation of China (Grant No. 10761012)theNatural Science Foundation of Yunnan Province,China (Grant No. 2003A002M) the Research GrantsCouncil of Hong Kong (Grant No. B-Q771)
文摘In general normed spaces, we consider a multiobjective piecewise linear optimization problem with the ordering cone being convex and having a nonempty interior. We establish that the weak Pareto optimal solution set of such a problem is the union of finitely many polyhedra and that this set is also arcwise connected under the cone convexity assumption of the objective function. Moreover, we provide necessary and sufficient conditions about the existence of weak (sharp) Pareto solutions.
文摘The problem whether every infinite dimensional Banach space has an infinite dimensional separable quotient space has remained unsolved for a long time. In this paper we prove: the Banach space X has an infinite dimensional separable quotient if and only if X has an infinite dimensional separable quasicomplemented subspace, also if and only if there exists a Banach space Y and a bounded linear operator T is an element of B(Y,X such that the range of T is nonclosed and dense in X. Besides, the other relevant questions for such spaces e.g. the question on operator ideals that on H.I.(hereditarily indecomposable) spaces, that on invariant subspaces of operators, etc, are also discussed.
基金Supported by the Science and Technology Foundation of Educational Committee of Tianjin (Grant No 20060402)
文摘Assume X is a normed space,every x ＊ ∈ S（X＊） can reach its norm at some point in B（X）,and Y is a β-normed space.If there is a quotient space of Y which is asymptotically isometric to l β,then L（X,Y） contains an asymptotically isometric copy of l β.Some sufficient conditions are given under which L（X,Y） fails to have the fixed point property for nonexpansive mappings on closed bounded β-convex subsets of L（X,Y）.
基金Supported by the National Natural Science Foundation of China (1 0 0 71 0 63 )the Founda-tion for University Key Teachers by the Ministry of Education of China
