# A generalization of the Schauder fixed point theorem via multivalued contractions

Paolo Cubiotti; Beatrice Di Bella

Commentationes Mathematicae Universitatis Carolinae (2001)

- Volume: 42, Issue: 4, page 637-640
- ISSN: 0010-2628

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topCubiotti, Paolo, and Di Bella, Beatrice. "A generalization of the Schauder fixed point theorem via multivalued contractions." Commentationes Mathematicae Universitatis Carolinae 42.4 (2001): 637-640. <http://eudml.org/doc/248813>.

@article{Cubiotti2001,

abstract = {We establish a fixed point theorem for a continuous function $f:X\rightarrow E$, where $E$ is a Banach space and $X\subseteq E$. Our result, which involves multivalued contractions, contains the classical Schauder fixed point theorem as a special case. An application is presented.},

author = {Cubiotti, Paolo, Di Bella, Beatrice},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {fixed points; multivalued contractions; absolute retracts; fixed points; multivalued contractions; absolute retracts},

language = {eng},

number = {4},

pages = {637-640},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {A generalization of the Schauder fixed point theorem via multivalued contractions},

url = {http://eudml.org/doc/248813},

volume = {42},

year = {2001},

}

TY - JOUR

AU - Cubiotti, Paolo

AU - Di Bella, Beatrice

TI - A generalization of the Schauder fixed point theorem via multivalued contractions

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 2001

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 42

IS - 4

SP - 637

EP - 640

AB - We establish a fixed point theorem for a continuous function $f:X\rightarrow E$, where $E$ is a Banach space and $X\subseteq E$. Our result, which involves multivalued contractions, contains the classical Schauder fixed point theorem as a special case. An application is presented.

LA - eng

KW - fixed points; multivalued contractions; absolute retracts; fixed points; multivalued contractions; absolute retracts

UR - http://eudml.org/doc/248813

ER -

## References

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- Hoffmann A., The distance to the intersection of two convex sets expressed by the distances to each of them, Math. Nachr. 157 (1992), 81-98. (1992) Zbl0773.52002MR1233049
- Klein E., Thompson A.C., Theory of Correspondences, John Wiley and Sons, New York, 1984. Zbl0556.28012MR0752692
- Ricceri B., Une propriété topologique de l'ensemble des points fixes d'une contraction multivoque à valeurs convexes, Atti Acc. Lincei Rend. Fis. 81 (8) (1987), 283-286. (1987) Zbl0666.47030MR0999821

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