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On properties of preinvex functions. (English) Zbl 1016.90056

Summary: We consider in this paper the class of preinvex functions introduced by T. Weir and B. Mond [ibid. 136, 29-38 (1988; Zbl 0663.90087)]; T. Weir and V. Jeyakumar [Bull. Aust. Math. Soc. 38, 177-189 (1988; Zbl 0639.90082)]. Under semi-continuity conditions, a determination of the satisfaction of preinvexity for a function can be achieved via an intermediate-point preinvexity check. A characterization of a preinvex function in terms of its relationship with an intermediate-point preinvexity and prequasi-invexity is provided.

MSC:

90C30 Nonlinear programming
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References:

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