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$$A$$-properness and fixed point theorems for dissipative type maps. (English) Zbl 0984.47038
Summary: We obtain new $$A$$-properness results for demicontinuous, dissipative type mappings defined only on closed convex subset 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 utilizing a theory of fixed point index.

##### MSC:
 47H06 Nonlinear accretive operators, dissipative operators, etc. 47H10 Fixed-point theorems 47H09 Contraction-type mappings, nonexpansive mappings, $$A$$-proper mappings, etc. 47H05 Monotone operators and generalizations 47J25 Iterative procedures involving nonlinear operators
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