Iterates of increasing linear operators, via Maia's fixed point theorem
Keywords:
Banach lattice, order unit, increasing linear operator, invariant linear partition of the space, fixed point, weakly Picard operator, Maia's fixed point theorem, functional differential equation.Abstract
Let X be a Banach lattice. In this paper we give conditions in which an increasing linear operator, A : X ! X is weakly Picard operator (see I.A. Rus, Picard operators and applications, Sc. Math. Japonicae, 58(2003), No. 1, 191-219). To do this we introduce the notion of \invariant linear partition of X with respect to A" and we use contraction principle and Maia's fixed point theorem. Some applications are also given.
Mathematics Subject Classification (2010): 47H10, 46B42, 47B65, 47A35, 34K06.
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