A result in best approximation theory. (English) Zbl 0676.41031

Sahab, S. A.; Khan, M. S.; Sessa, S.

J. Approximation Theory 55, No. 3, 349-351 (1988).

Let T, I be two commuting operators on a subset c of a Banach space X, and let F(T) (respectively F(I)) be the set of fixed points of T (respectively I). For \(\bar x\in F(T)\cap F(I)\), D denotes the set of best approximation elements of \(\bar x\) in C. The authors prove that \(D\cap F(T)\cap F(I)\) is non-empty if C, F and I satisfies certain conditions. If the operator I is the identity on X, one obtains a result of S. P. Singh [J. Approximation Theory 25, 89-90 (1979; Zbl 0399.41032)].

Reviewer: I.Şerb

MSC:

41A50	Best approximation, Chebyshev systems
41A65	Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
47H10	Fixed-point theorems

Keywords:

set of best approximation elements

Citations:

Zbl 0399.41032

References:

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