### Iterative solution of nonlinear equations of Hammerstein type.

Zegeye, H. (2003)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

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Zegeye, H. (2003)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

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Athanassios Kartsatos (1995)

Studia Mathematica

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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 \overline{T\left(\partial G\right)}=\varnothing $. Then $M\subset \overline{TG}$. If, moreover, Case (i) or (ii) holds and T is of type $\left({S}_{1}\right)$, or Case (iii) holds and T is of type $\left({S}_{2}\right)$, then M ⊂ TG. Various results...

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