# Sets in the ranges of nonlinear accretive operators in Banach spaces

Studia Mathematica (1995)

- Volume: 114, Issue: 3, page 261-273
- ISSN: 0039-3223

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topKartsatos, Athanassios. "Sets in the ranges of nonlinear accretive operators in Banach spaces." Studia Mathematica 114.3 (1995): 261-273. <http://eudml.org/doc/216191>.

@article{Kartsatos1995,

abstract = {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 $M ∩ \overline\{T(∂ G)\} = ∅$. Then $M ⊂ \overline\{TG\}$. 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 of Morales, Reich and Torrejón, and the author are improved and/or extended.},

author = {Kartsatos, Athanassios},

journal = {Studia Mathematica},

keywords = {accretive operator; m-accretive operator; compact perturbations; compact resolvents; Leray-Schauder boundary condition; mapping theorems; -accretive operator; Leray- Schauder boundary condition; demicontinuous},

language = {eng},

number = {3},

pages = {261-273},

title = {Sets in the ranges of nonlinear accretive operators in Banach spaces},

url = {http://eudml.org/doc/216191},

volume = {114},

year = {1995},

}

TY - JOUR

AU - Kartsatos, Athanassios

TI - Sets in the ranges of nonlinear accretive operators in Banach spaces

JO - Studia Mathematica

PY - 1995

VL - 114

IS - 3

SP - 261

EP - 273

AB - 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 $M ∩ \overline{T(∂ G)} = ∅$. Then $M ⊂ \overline{TG}$. 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 of Morales, Reich and Torrejón, and the author are improved and/or extended.

LA - eng

KW - accretive operator; m-accretive operator; compact perturbations; compact resolvents; Leray-Schauder boundary condition; mapping theorems; -accretive operator; Leray- Schauder boundary condition; demicontinuous

UR - http://eudml.org/doc/216191

ER -

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