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

We use the method of monotone iterations to obtain fixed point and coupled\nfixed point results for mixed monotone operators in the setting of partially\nordered sets, with no additional assumptions on the partial order and with no\nconvergence structure. We define the concept of attractive fixed point with\nrespect to the partial order and obtain several criteria for the existence,\nuniqueness and order-attractiveness of the fixed points, both in the presence\nand in the absence of a coupled lower-upper fixed point. As an application, we\npresent a fixed point result for a class of mixed monotone operators in the\nsetting of ordered linear spaces.\n