Let

$F$ and

$K$ be nonempty subsets of

$X$ and

$f:X\times X\to \mathbb{R}$. In this paper the author studies the notion of

$f$-best simultaneous approximation to

$F$ from

$K$. The concept is associated with the notion of best simultaneous approximation in normed linear spaces. Adopting

$X$ variously, such as a topological space, a topological vector space, a vector space, or just a non-empty set, several theorems are given. Most of the results of

*P. Govindarajulu* [J. Math. Phys. Sci. 22, No. 6, 789-796 (1988;

Zbl 0745.41018)] are deduced a consequences of results obtained here. An example given here shows that certain claims made by P. Govindarajulu (loc. cit) is false.