| 个人简介 | |
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 Prof. Dong Yun Shin University of Seoul, South Korea |
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| 标题： Additive functional inequalities in matrix normed spaces and applications | |
| 摘要： In this talk, we prove the Hyers-Ulam stability of the Cauchy additive functional inequality in matrix normed modules over a C*-algebra. For a mapping f:X→Y, define D_u f_n:M_n(X^2)→M_n(Y) by D_u f_n([x_ij+y_ij])-uf_n([x_ij])-uf_n([y_ij]) for all unitary u and all x=[x_ij],y=[y_ij]∈M_n(X). Here h_n: M_n(X)→M_n(Y) is defined by h_n([x_ij])=[h(x_ij)]. Theorem A. Let f:X→Ybe a mapping and φ:X^2→[0,∞) a function such that Ψ(a,b): = 1/2 ∑_(l=0)^∞▒〖φ(2^(l ) 〗 a,2^l b)< ∞∑_(l=0)^∞, || D_u f_n([x_ij],[y_ij])||≤∑_(i,j=1)^n▒〖φ(〗 x_ij,y_ij) for all a,b∈ X,u∈U(A) and all x=[x_ij],y=[y_ij]∈M_n(X). Then there exists a unique A-linear mapping L:X→Y such that ‖f_n([x_ij])-L_n([x_ij])‖≤∑_(i,j=1)^n▒Ψ(x_ij,y_ij) forall x=[x_ij]∈M_n(X). | |
| 简介：
Dong Yun Shin is working as a professor at department of Mathematics, University of Seoul.He has accomplished her doctoral degree in Mathematics from Seoul National University. He is interested in functional analysis and his main research topics include operator algebras, functional inequalities, functional equations, fixed point theory and fuzzy mappings. He is working for several journals such as Korean Journal of Mathematics and Journal of Korean Mathematical Education, Series B as section editors on Functional Analysis.He has been working for the Korean Mathematical Society, Mathematics Educationand Mathematics Educations for Gifted Children. He has published several books such as middle school mathematics text books,text books for universityand books for general people. He has also published a number of articles on international journals related to operator algebras, operator matrix spaces, functional inequalities andequations, fixed point theory, random normed space and fuzzy mappings.
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