In this paper, we give four general results on linear extension of isometries between the unit spheres in β-normed spaces. These results improve the corresponding theorems in β-normed spaces.
In this paper, we investigate the Hyers-Ulam stability of the following function equation 2f（2x ＋ y） ＋ 2f（2x - y） = 4f（x ＋ y） ＋ 4f（x - y） ＋ 4f（2x） ＋ f（2y） - Sf（x） - 8f（y） in quasi-β-normed spaces.
This paper deals with the problems of best approximation inβ-normed spaces. With the tool of conjugate cone introduced in[1]and via the Hahn-Banach extension theorem of β-subseminorm in[2],the characteristics that a...This paper deals with the problems of best approximation inβ-normed spaces. With the tool of conjugate cone introduced in[1]and via the Hahn-Banach extension theorem of β-subseminorm in[2],the characteristics that an element in a closed subspace is the best approximation are given in Section 2.It is obtained in Section 3 that all convex sets or subspaces of aβ-normed space are semi-Chebyshev if and only if the space is itself strictly convex.The fact that every finite dimensional subspace of a strictly convexβ-normed space must be Chebyshev is proved at last.展开更多
In this paper, we introduce the following quattuordecic functional equation f(x+7y)-14f(x+6y)+91f(x+5y)-364f(x+4y)+1001f(x+3y)-2002f(x+2y)+3003f(x+y)-3432f(x)+3003f(x-y)-2002f(x-2y)+1001f(x-3y)-364f(x-4y)+91f(x-5y)-14...In this paper, we introduce the following quattuordecic functional equation f(x+7y)-14f(x+6y)+91f(x+5y)-364f(x+4y)+1001f(x+3y)-2002f(x+2y)+3003f(x+y)-3432f(x)+3003f(x-y)-2002f(x-2y)+1001f(x-3y)-364f(x-4y)+91f(x-5y)-14f(x-6y)+f(x-7y)=14!f(y), investigate the general solution and prove the stability of this quattuordecic functional equation in quasi β-normed spaces by using the fixed point method.展开更多
We get the characterizations of the family of all nonnegative, subadditive,β-absolutely homogeneous and continuous functionals defined on X, when the ;3-normed space X contains an asymptotically isometric copy of l^...We get the characterizations of the family of all nonnegative, subadditive,β-absolutely homogeneous and continuous functionals defined on X, when the ;3-normed space X contains an asymptotically isometric copy of l^β. Moreover, it is proved that if a closed bounded β-convex subset K of a β-normed space contains an asymptotically isometric β-basis, then K contains a closed β-convex subset C which fails the fixed point property.展开更多
文摘In this paper, we give four general results on linear extension of isometries between the unit spheres in β-normed spaces. These results improve the corresponding theorems in β-normed spaces.
基金Supported by National Science Foundation of China (Grant Nos. 10626031 and 10971117) the Scientific Research Project of the Department of Education of Shandong Province (Grant No. J08LI15)
文摘In this paper, we investigate the Hyers-Ulam stability of the following function equation 2f（2x ＋ y） ＋ 2f（2x - y） = 4f（x ＋ y） ＋ 4f（x - y） ＋ 4f（2x） ＋ f（2y） - Sf（x） - 8f（y） in quasi-β-normed spaces.
基金the Foundation of the Education Department of Jiangsu Province(No.05KJB110001)
文摘This paper deals with the problems of best approximation inβ-normed spaces. With the tool of conjugate cone introduced in[1]and via the Hahn-Banach extension theorem of β-subseminorm in[2],the characteristics that an element in a closed subspace is the best approximation are given in Section 2.It is obtained in Section 3 that all convex sets or subspaces of aβ-normed space are semi-Chebyshev if and only if the space is itself strictly convex.The fact that every finite dimensional subspace of a strictly convexβ-normed space must be Chebyshev is proved at last.
文摘In this paper, we introduce the following quattuordecic functional equation f(x+7y)-14f(x+6y)+91f(x+5y)-364f(x+4y)+1001f(x+3y)-2002f(x+2y)+3003f(x+y)-3432f(x)+3003f(x-y)-2002f(x-2y)+1001f(x-3y)-364f(x-4y)+91f(x-5y)-14f(x-6y)+f(x-7y)=14!f(y), investigate the general solution and prove the stability of this quattuordecic functional equation in quasi β-normed spaces by using the fixed point method.
基金Supported by the Science and Technology Foundation of Educational Committee of Tianjin (Grant No.20060402)
文摘We get the characterizations of the family of all nonnegative, subadditive,β-absolutely homogeneous and continuous functionals defined on X, when the ;3-normed space X contains an asymptotically isometric copy of l^β. Moreover, it is proved that if a closed bounded β-convex subset K of a β-normed space contains an asymptotically isometric β-basis, then K contains a closed β-convex subset C which fails the fixed point property.
