Displaying similar documents to “Iterative approximation of solutions of nonlinear equations of Hammerstein type.”

Sets in the ranges of nonlinear accretive operators in Banach spaces

Athanassios Kartsatos (1995)

Studia Mathematica


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 T ( G ) ¯ = . Then M 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...