Volume 1, Issue 3
An L_1 Minimizzation Problem by Generalized Rational Functions
DOI:

J. Comp. Math., 1 (1983), pp. 243-246

Published online: 1983-01

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• Abstract

Let P,Q $\subset L_1(X,\Sigma,\mu)$ and q(x)>0 a.e. in X for all $q\in Q$. Define R={p/q:$p\in P,q\in Q$}. In this paper we discuss and $L_1$ minimization problem of a nonnegative function E(z,x), i.e. we wish to find a minimum of the functional $\phi(r)=\int _X qE(r,x)d\mu$ form r=p/q $\in R$. For such a problem we have established the complete characterizations of its minimum and of uniquneness of its minimum, when both P,Q are arbitary convex subsets.

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@Article{JCM-1-243, author = {Ying-Guang Shi}, title = {An L_1 Minimizzation Problem by Generalized Rational Functions}, journal = {Journal of Computational Mathematics}, year = {1983}, volume = {1}, number = {3}, pages = {243--246}, abstract = { Let P,Q $\subset L_1(X,\Sigma,\mu)$ and q(x)>0 a.e. in X for all $q\in Q$. Define R={p/q:$p\in P,q\in Q$}. In this paper we discuss and $L_1$ minimization problem of a nonnegative function E(z,x), i.e. we wish to find a minimum of the functional $\phi(r)=\int _X qE(r,x)d\mu$ form r=p/q $\in R$. For such a problem we have established the complete characterizations of its minimum and of uniquneness of its minimum, when both P,Q are arbitary convex subsets. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9700.html} }
TY - JOUR T1 - An L_1 Minimizzation Problem by Generalized Rational Functions AU - Ying-Guang Shi JO - Journal of Computational Mathematics VL - 3 SP - 243 EP - 246 PY - 1983 DA - 1983/01 SN - 1 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9700.html KW - AB - Let P,Q $\subset L_1(X,\Sigma,\mu)$ and q(x)>0 a.e. in X for all $q\in Q$. Define R={p/q:$p\in P,q\in Q$}. In this paper we discuss and $L_1$ minimization problem of a nonnegative function E(z,x), i.e. we wish to find a minimum of the functional $\phi(r)=\int _X qE(r,x)d\mu$ form r=p/q $\in R$. For such a problem we have established the complete characterizations of its minimum and of uniquneness of its minimum, when both P,Q are arbitary convex subsets.