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Fixed point theorems in best approximation theory. (English) Zbl 0834.54026
Using some ideas of the paper by the first author [Proc. Am. Math. Soc. 103, No. 3, 977-983 (1988; Zbl 0661.54043)], the authors prove a new fixed point theorem. Applying this theorem they obtain a result in best approximation theory which generalizes an earlier one from the paper [S. A. Sahab, M. S. Khan and the second author, J. Approximation Theory 55, 349-351 (1988; Zbl 0676.41031)]. A similar result is given for Banach spaces satisfying the Opial condition.

54H25 Fixed-point and coincidence theorems (topological aspects)
47H10 Fixed-point theorems
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