Fixed Points of Multivalued Contractions
Funkcionalʹnyj analiz i ego priloženiâ, Tome 36 (2002) no. 2, pp. 89-92.

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A fixed-point theorem is proved for a broad class of closed-valued $k(\;\cdot\;)$-contractions with $\limsup_{s\to t+0}k(s)1$ for any positive $t$ and with $\limsup_{s\to0+0}k(s)=1$.
Keywords: multivalued contraction, fixed point, Reich's problem, $G$-summable function.
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P. V. Semenov. Fixed Points of Multivalued Contractions. Funkcionalʹnyj analiz i ego priloženiâ, Tome 36 (2002) no. 2, pp. 89-92. http://geodesic.mathdoc.fr/item/FAA_2002_36_2_a11/

[1] Daffer P. Z., Kaneko H., “Fixed points of generalized contractive multi-valued mappings”, J. Math. Anal. Appl., 192 (1995), 655–666 | DOI | MR | Zbl

[2] Mizoguchi N., Takahashi W., “Fixed point theorems for multivalued mappings on complete metric spaces”, J. Math. Anal. Appl., 141 (1989), 177–188 | DOI | MR | Zbl

[3] Reich S., “Fixed points of contractive functions”, Boll. Un. Mat. Ital. (4), 5 (1972), 26–42 | MR | Zbl

[4] Reich S., “Some fixed point problems”, Atti. Accad. Naz. Lincei, 57 (1974), 194–198 | MR

[5] Reich S., “Some problems and results in fixed point theory”, Topological methods in nonlinear functional analysis (Toronto, Ont., 1982), Contemp. Math., 21, Amer. Math. Soc., Providence, RI, 1983, 179–187 | DOI | MR

[6] Semenov P. V., “Teoremy o nepodvizhnoi tochke pri kontroliruemom otkaze ot vypuklosti znachenii mnogoznachnogo otobrazheniya”, Matem. sb., 189:3 (1998), 141–160 | DOI | MR | Zbl

[7] Repovs D., Semenov P. V., “On functions of nonconvexity for graphs of continuous functions”, J. Math. Anal. Appl., 196 (1995), 1021–1029 | DOI | MR | Zbl

[8] Chang T. H., Math. Japonica, 41 (1995), 311–320 | MR | Zbl