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On Semi- -Preinvex Functions

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  • Xiaoling Liu
  • D. H. Yuan

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.

Suggested Citation

  • Xiaoling Liu & D. H. Yuan, 2012. "On Semi- -Preinvex Functions," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-13, January.
    • Handle: RePEc:hin:jnlaaa:530468
    DOI: 10.1155/2012/530468
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