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**Characterizations and applications of prequasi-invex functions.**
*(English)*
Zbl 1064.90038

Summary: In this paper, two new types of generalized convex functions are introduced. They are called strictly prequasi-invex functions and semistrictly prequasi-invex functions. Note that prequasi-invexity does not imply semistrict prequasi-invexity. The characterization of prequasi-invex functions is established under the condition of lower semicontinuity, upper semicontinuity, and semistrict prequasi-invexity, respectively. Furthermore, the characterization of semistrictly prequasi-invex functions is also obtained under the condition of prequasi-invexity and lower semicontinuity, respectively. A similar result is also obtained for strictly prequasi-invex functions. It is worth noting that these characterizations reveal various interesting relationships among prequasi-invex, semistrictly prequasi-invex, and strictly prequasi-invex functions. Finally, prequasi-invex, semistrictly prequasi-invex, and strictly prequasi-invex functions are used in the study of optimization problems.

### Keywords:

Prequasi-invex functions; strictly prequasi-invex functions; semistrictly prequasi-invex functions; semicontinuity
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\textit{X. M. Yang} et al., J. Optim. Theory Appl. 110, No. 3, 645--668 (2001; Zbl 1064.90038)

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