An application of a fixed point theorem to best approximation

The object of this paper is twofold. First, certain fixed point theorems of Dotson [1] are generalized (Theorems 1, 2) by an appeal to an earlier result of this author [5]. Second, one of these theorems is utilized to obtain a theorem (Theorem 3) on best approximations which incidentally generalizes a result of Meinardus ([3], Theorem). This theorem has interesting applications brought out in its corollaries, and its proof reveals how the original proof of Meinardus can be considerably simplified with no appeal to algebraic-topological ideas implicit in Schauder's fixed point theorem. © 1977.