be nonempty subsets of
. In this paper the author studies the notion of
-best simultaneous approximation to
. The concept is associated with the notion of best simultaneous approximation in normed linear spaces. Adopting
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.