$A$-properness and fixed point theorems for dissipative type maps

Abstract

We obtain new $A$-properness results for demicontinuous, dissipative type mappings defined only on closed convex subsets of a Banach space $X$ with uniformly convex dual and which satisfy a property called weakly inward. The method relies on a new property of the duality mapping in such spaces. New fixed point results are obtained by utilising a theory of fixed point index.