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On best simultaneous approximation. (English) Zbl 0794.41007
Let F and K be nonempty subsets of X and f:X×X. 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.
41A28Simultaneous approximation
41A50Best approximation, Chebyshev systems
41A52Uniqueness of best approximation
54H99Connections of general topology with other structures
46A99Topological linear spaces