This article is cited in 13 papers

On the Lamé point and its generalizations in a normed space

A. L. Garkavi, V. A. Shmatkov


Abstract: Existence and uniqueness conditions are investigated for an element $y^*$ which belongs to a subset $G$ of a normed linear space $E$ and minimizes the following functional over $G$:
$$ F(y)=\int_A e(x-y)\,\mu(dx), $$
where $e(x)$ is a functional given on $E$ and bounded from below, $A$ is a Borel subset of $E$, and $\mu$ is a measure defined on the $\sigma$-algebra of the Borel subsets of $A$.
Bibliography: 16 titles.

UDC: 513.881+519.3

MSC: Primary 49A30; Secondary 49A50

Received: 30.10.1973

 English version: Mathematics of the USSR-Sbornik, 1974, 24:2, 267–286

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