Geodesic
The existence of fixed points of left-continuous monotone operators in spaces with a~regular cone
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2011), pp. 40-47.

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In theorems on the existence of a fixed point of an operator the latter is usually assumed to be continuous. In this paper we prove a theorem with sufficient conditions for the existence of a fixed point of an operator which is not necessarily continuous (possibly it is left-continuous). The obtained theorem with the use of regular cones is applied for proving the existence of a fixed point of a nonliner integral operator. We give an example illustrating the theorem.
Keywords: left-continuous operator, cone in a Banach space, fixed point of an operator. 
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     author = {E. Yu. Elenskaya},
     title = {The existence of fixed points of left-continuous monotone operators in spaces with a~regular cone},
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E. Yu. Elenskaya. The existence of fixed points of left-continuous monotone operators in spaces with a~regular cone. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2011), pp. 40-47. http://geodesic.mathdoc.fr/item/IVM_2011_10_a4/

[1] Filippov A. F., Differentsialnye uravneniya s razryvnoi pravoi chastyu, Nauka, M., 1985 | MR

[2] Birkgof G., Teoriya struktur, In. lit., M., 1952

[3] Krasnoselskii M. A., Polozhitelnye resheniya operatornykh uravnenii, Fizmatgiz, M., 1962 | MR

[4] Engibaryan N. B., “O nepodvizhnoi tochke monotonnogo operatora v kriticheskom sluchae”, Izv. RAN. Ser. matem., 70:5 (2006), 79–96 | MR | Zbl

[5] Krasnoselskii M. A., Vainikko G. M., Zabreiko P. P. i dr., Priblizhennoe reshenie operatornykh uravnenii, Nauka, M., 1969 | MR