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In this paper we study the existence and uniqueness of a solution for minimization problems with generic increasing functions in an ordered Banach space X. The standard approaches are not suitable in such a setting. We propose a new type of perturbation adjusted for the problem under consideration, prove the existence and point out sufficient conditions providing the uniqueness of a solution. These results are proved by assuming that the space X enjoys the following property: each decreasingdoi:10.1017/s1446788700000884 fatcat:yq2l3f5w7fbz3iety77oicu7ni