Abstract
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 nonlinear integral operator. We give an example illustrating the theorem.
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Original Russian Text © E.Yu. Elenskaya, 2011, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2011, No. 10, pp. 40–47.
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Elenskaya, E.Y. The existence of fixed points of left-continuous monotone operators in spaces with a regular cone. Russ Math. 55, 34–40 (2011). https://doi.org/10.3103/S1066369X11100057
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DOI: https://doi.org/10.3103/S1066369X11100057