A Characterization of Nonlinear ...-Accretive Operators.

Simeon Reich

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Let X be a real Banach space and G ⊂ X open and bounded. Assume that one of the following conditions is satisfied: (i) X* is uniformly convex and T:Ḡ→ X is demicontinuous and accretive; (ii) T:Ḡ→ X is continuous and accretive; (iii) T:X ⊃ D(T)→ X is m-accretive and Ḡ ⊂ D(T). Assume, further, that M ⊂ X is pathwise connected and such that M ∩ TG ≠ ∅ and $M \cap \bar{T (\partial G)} = \emptyset$ . Then $M \subset \bar{T G}$ . If, moreover, Case (i) or (ii) holds and T is of type $(S_{1})$ , or Case (iii) holds and T is of type $(S_{2})$ , then M ⊂ TG. Various results...