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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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