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Remarks on invariant approximations. (English) Zbl 1077.41022
Summary: We provide a positive answer to M. A. Al-Thagafi’s open question [J. Approximation Theory 85, No. 3, 318–323 (1996; Zbl 0858.41022)] in the setting of Banach spaces. Our result extends the well-known results of A. Smoluk [Ann. Soc. Math. Pol., Ser. III, Mat. Stosow. 17, 17–22 (1981; Zbl 0539.41038)] and L. Habiniak [J. Approximation Theory 56, No. 3, 241–244 (1989; Zbl 0673.41037].

41A50 Best approximation, Chebyshev systems
47H10 Fixed-point theorems
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