Volume 4,  Issue 3 (GI8), 2003

Article 57

NEW NORM TYPE INEQUALITIES FOR LINEAR MAPPINGS

SABUROU SAITOH

DEPARTMENT OF MATHEMATICS,
FACULTY OF ENGINEERING, 
GUNMA UNIVERSITY, 
KIRYU 376-8515, JAPAN
E-Mail: ssaitoh@math.sci.gunma-u.ac.jp

Received 09 December, 2002; Accepted 02 July, 2003.
Communicated by: S.S. Dragomir

ABSTRACT.   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.
Key words:
Learning theory, Convergence rate, Approximation, Reproducing kernel, Hilbert space, Linear mapping, Norm inequality

2000 Mathematics Subject Classification:
Primary 68T05, 30C40, 44A05, 35A22.

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Other papers in this issue

Report of the General Inequalities 8 Conference; September 15-21, 2002, Noszvaj, Hungary
Compiled by Zsolt Páles

Convolution Inequalities and Applications
Saburou Saitoh, Vu Kim Tuan and Masahiro Yamamoto

The Hardy-Landau-Littlewood Inequalities with Less Smoothness
Constantin P. Niculescu and Constantin Buse

Continuity Properties of Convex-type Set-Valued Maps
Kazimierz Nikodem

Carleman's Inequality - History, Proofs and Some New Generalizations
Maria Johansson, Lars-Erik Persson and Anna Wedestig

Andersson's Inequality and Best Possible Inequalities
A.M. Fink  

On Some Results Involving the Cebysev Functional and its Generalisations
P. Cerone

Separation and Disconjugacy
R.C. Brown

New Norm Type Inequalities for Linear Mappings
Saburou Saitoh

An Integral Approximation in Three Variables
A. Sofo

On Some Spectral Results Relating to the Relative Values of Means
C.E.M. Pearce

On Zeros of Reciprocal Polynomials of Odd Degree
Piroska Lakatos and László Losonczi

Some New Hardy Type Inequalities and their Limiting Inequalities
Anna Wedestig

Generalizations of the Triangle Inequality
Saburou Saitoh

A Survey on Cauchy-Bunyakovsky-Schwarz Type Discrete Inequalities
S.S. Dragomir
 

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