The method of monotone iterations for mixed monotone operators in partially ordered sets and order-attractive fixed points

摘要

We use the method of monotone iterations to obtain fixed point and coupled fixed pointresults for mixed monotone operators in the setting of partially ordered sets, with no additionalassumptions on the partial order and with no convergence structure. We define the concept ofattractive fixed point with respect to the partial order and obtain several criteria for the existence,uniqueness and order-attractiveness of the fixed points, both in the presence and in the absence ofa coupled lower-upper fixed point. As an application, we present a fixed point result for a class ofmixed monotone operators in the setting of ordered linear spaces.