On the Lamé point and its generalizations in a normed space

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.