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Applications of fixed point theorems to invariant approximation. (English) Zbl 0995.41018

The authors extend some fixed point theorems due to D. E. Anderson, J. L. Nelson and K. L. Singh [Math. Jap. 31, 665-672 (1986; Zbl 0606.47058)] and S. A. Sahab, M. S. Khan and S. Sessa [J. Approximation Theory 55, 349-351 (1988; Zbl 0676.41031)] to a locally bounded topological vector space (\(lbtrs\)). Some Brosowski-Meinardus type theorems for nonexpansive maps defined on a class of nonconvex sets containing the subclass of starshaped sets in \(lbtrs\) which is not necessarily locally convex have been obtained.

MSC:

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