A result in best approximation theory of the second author [J.Approx. Theory 55, no.3 (1988), 349-351] is generalized by using a fixed point theorem of the first author [Proc. Amer. Math. Soc. 103, No. 3 (1988), 977-983]. A similar result is given in Banach spaces satisfying Opial's Condition.
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