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. 
@article{IVM_2011_10_a4,
     author = {E. Yu. Elenskaya},
     title = {The existence of fixed points of left-continuous monotone operators in spaces with a~regular cone},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {40--47},
     publisher = {mathdoc},
     number = {10},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2011_10_a4/}
}
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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/