The best recovery of a linear functional Lf, f=f(x,y), on the basis of given linear functionals L jf,j=1,2,...,N in a sense of Sard has been investigated, using analogy of Peano's theorem. The best recovery of a ...The best recovery of a linear functional Lf, f=f(x,y), on the basis of given linear functionals L jf,j=1,2,...,N in a sense of Sard has been investigated, using analogy of Peano's theorem. The best recovery of a bivariate function by given scattered data has been obtained in a simple analytical form as a special case.展开更多
The concept of FC-closed subset in FC-space without any linear structure was introduced. Then, the generalized KKM theorem is proved for FC-closed value mappings under some conditions. The FC-space in the theorem is t...The concept of FC-closed subset in FC-space without any linear structure was introduced. Then, the generalized KKM theorem is proved for FC-closed value mappings under some conditions. The FC-space in the theorem is the generalization of L-convex space and the condition of the mapping with finitely FC-closed value is weaker than that with finitely L-closed value.展开更多
The aim of this paper is to establish an extension of qualitative and quantitative uncertainty principles for the Fourier transform connected with the spherical mean operator.
In this paper, we establish some new generalized KKM-type theorems based on weakly generalized KKM mapping without any convexity structure in topological spaces. As applications, some minimax inequalities and an exist...In this paper, we establish some new generalized KKM-type theorems based on weakly generalized KKM mapping without any convexity structure in topological spaces. As applications, some minimax inequalities and an existence theorem of equilibrium points for an abstract generalized vector equilibrium problem are proved in topological spaces. The results presented in this paper unify and generalize some known results in recent literature.展开更多
The boundedness of all solutions is shown for Duffing type equationsd 2xd t 2+x 2n+1 +2nj=0x jp j(t)=0, n≥1,where p 1,p 2,...,p 2n are of period 1 and of Lipschitzian continuity and p n+1 ,...,p 2n are of Zygmundian ...The boundedness of all solutions is shown for Duffing type equationsd 2xd t 2+x 2n+1 +2nj=0x jp j(t)=0, n≥1,where p 1,p 2,...,p 2n are of period 1 and of Lipschitzian continuity and p n+1 ,...,p 2n are of Zygmundian continuity. This conclusion implies that the boundedness phenomenon for the Duffing type equations does not require the smoothness in the time variable, thus answering the question posed by Dieckerhoff and Zehnder.展开更多
文摘The best recovery of a linear functional Lf, f=f(x,y), on the basis of given linear functionals L jf,j=1,2,...,N in a sense of Sard has been investigated, using analogy of Peano's theorem. The best recovery of a bivariate function by given scattered data has been obtained in a simple analytical form as a special case.
文摘The concept of FC-closed subset in FC-space without any linear structure was introduced. Then, the generalized KKM theorem is proved for FC-closed value mappings under some conditions. The FC-space in the theorem is the generalization of L-convex space and the condition of the mapping with finitely FC-closed value is weaker than that with finitely L-closed value.
文摘The aim of this paper is to establish an extension of qualitative and quantitative uncertainty principles for the Fourier transform connected with the spherical mean operator.
基金Supported by the National Natural Science Foundation of China (No. 10771058)the Hunan Provincial Natural Science Foundation (No. 09JJ6013)
文摘In this paper, we establish some new generalized KKM-type theorems based on weakly generalized KKM mapping without any convexity structure in topological spaces. As applications, some minimax inequalities and an existence theorem of equilibrium points for an abstract generalized vector equilibrium problem are proved in topological spaces. The results presented in this paper unify and generalize some known results in recent literature.
文摘The boundedness of all solutions is shown for Duffing type equationsd 2xd t 2+x 2n+1 +2nj=0x jp j(t)=0, n≥1,where p 1,p 2,...,p 2n are of period 1 and of Lipschitzian continuity and p n+1 ,...,p 2n are of Zygmundian continuity. This conclusion implies that the boundedness phenomenon for the Duffing type equations does not require the smoothness in the time variable, thus answering the question posed by Dieckerhoff and Zehnder.
