# 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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## Abstract

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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 of Morales, Reich and Torrejón, and the author are improved and/or extended.

## How to cite

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Kartsatos, 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 -

## References

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25. [25] R. Torrejón, Some remarks on nonlinear functional equations, in: Contemp. Math. 18, Amer. Math. Soc., 1983, 217-246. Zbl0518.47042

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