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We use the method of monotone iterations to obtain fixed point and coupledfixed point results for mixed monotone operators in the setting of partiallyordered sets, with no additional assumptions on the partial order and with noconvergence structure. We define the concept of attractive fixed point withrespect to the partial order and obtain several criteria for the existence,uniqueness and order-attractiveness of the fixed points, both in the presenceand in the absence of a coupled lower-upper fixed point. As an application, wepresent a fixed point result for a class of mixed monotone operators in thesetting of ordered linear spaces.

The Method of Monotone Iterations for Mixed Monotone Operators in Partially Ordered Sets and Order-Attractive Fixed Points