SOME GENERALIZATIONS OF KY FAN''''S BEST APPROXIMATION THEOREM

We pressent new Ky Fan type best approximation theorems for a discontinuous multivalued map on metrizable topological vector spaces and hyperconvex spaces. In addition, fixed point results are derived for the map studied. Our work generalizes severl results in approximation theory.     

Classroom note: A Generalization of Leibniz rule for higher derivatives

This note provides a simple method to extend the usual Leibniz rule for higher derivatives of the product of two functions to several functions, which is within the reach of freshman calculus students.     

On the equivalence of the Heine-Borel and the Bolzano-Weierstrass theorems

The equivalence of the Heine-Borel theorem and the Bolzano-Weierstrass theorem is proved.     

SOME GENERALIZATIONS OF KY FAN＇S BEST APPROXIMATION THEOREM

We pressent new Ky Fan type best approximation theorems for a discontinuous multivalued map onmetrizable topological vector spaces and hyperconvex spaces. In addition, fixed point results are derivedfor the map studied. Our work generalizes severl results in approximation theory.     

Applications of fixed point theorems to invariant approximation

We prove some fixed point theorems. As applications we obtain Brosowski-Meinardus type theorems on invariant approximations on a class of nonconvex sets in locally bounded topological vector spaces.