## 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

### Keywords:

fixed point theorem; Brosowski-Meinardus type

### Citations:

Zbl 0606.47058; Zbl 0676.41031