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.


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