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  Volume 4, Issue 3, Article 57
New Norm Type Inequalities for Linear Mappings

    Authors: Saburou Saitoh,  
    Keywords: Learning theory, Convergence rate, Approximation, Reproducing kernel, Hilbert space, Linear mapping, Norm inequality  
    Date Received: 09/12/02  
    Date Accepted: 02/07/03  
    Subject Codes:

68T05, 30C40, 44A05, 35A22.

    Editors: Sever S. Dragomir,  

In this paper, in connection with a basic formula by S. Smale and D. X. Zhou which is fundamental in the approximation error estimates in statistical learning theory, we give new norm type inequalities based on the general theory of reproducing kernels combined with linear mappings in the framework of Hilbert spaces. We shall give typical concrete examples which may be considered as new norm type inequalities and have physical meanings.

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