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On Semi--Preinvex Functions

DOI: 10.1155/2012/530468

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Abstract:

We firstly construct a concrete semi-invex set which is not invex. Basing on concept of semi-invex set, we introduce some kinds of generalized convex functions, which include semi-(,)-preinvex functions, strictly semi-(,)-preinvex functions and explicitly semi-(,)-preinvex functions. Moreover, we establish relationships between our new generalized convexity and generalized convexity introduced in the literature. With these relationships and the well-known results pertaining to common generalized convexity, we obtain results for our new generalized convexities. We extend the existing results in the literature.

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