This article is cited in 1 paper

The existence of fixed points of left-continuous monotone operators in spaces with a regular cone

E. Yu. Elenskaya

Chair of Mathematical Analysis, Perm State University, Perm, Russia

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 nonliner integral operator. We give an example illustrating the theorem.

Keywords: left-continuous operator, cone in a Banach space, fixed point of an operator.

UDC: 517.988

Received: 14.07.2010

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2011, 55:10, 34–40

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