Geodesic
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. 
@article{FAA_2002_36_2_a11,
     author = {P. V. Semenov},
     title = {Fixed {Points} of {Multivalued} {Contractions}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {89--92},
     publisher = {mathdoc},
     volume = {36},
     number = {2},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2002_36_2_a11/}
}
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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/