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New classes of mappings, called cyclic (noncyclic) condensing operators, are introduced and used to
investigate the existence of best proximity points (best proximity pairs) with the help of a suitable measure
of noncompactness. In this way, we obtain some real generalizations of Schauder and Darboï¿½??s fixed point
theorems. In the last section, we apply such results to study the existence of optimum solutions to a system
of differential equations.
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