October  2014, 10(4): 1319-1321. doi: 10.3934/jimo.2014.10.1319

A note on preinvexity

1. 

Department of Mathematics, Chongqing Normal University, Chongqing 400047

Received  August 2013 Revised  September 2013 Published  February 2014

In this note, we obtain an important property from Condition $C$. Using the property, we can provide short proofs for some properties of (generalized) preinvex functions.
Citation: Xinmin Yang. A note on preinvexity. Journal of Industrial & Management Optimization, 2014, 10 (4) : 1319-1321. doi: 10.3934/jimo.2014.10.1319
References:
[1]

S. R. Mohan and S. K. Neogy, On invex sets and preinvex functions,, Journal of Mathematical Analysis and Applications, 189 (1995), 901.  doi: 10.1006/jmaa.1995.1057.  Google Scholar

[2]

X. M. Yang, X. Q. Yang and K. L. Teo, Characterizations and applications of prequasi-invex functions,, Journal of Optimization Theory and Applications, 110 (2001), 645.  doi: 10.1023/A:1017544513305.  Google Scholar

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X. M. Yang, X. Q. Yang and K. L. Teo, Generalized invexity and generalized invariant monotonicity,, Journal of Optimization Theory and Applications, 117 (2003), 607.  doi: 10.1023/A:1023953823177.  Google Scholar

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X. M. Yang, X. Q. Yang and K. L. Teo, Criteria for generalized invex monotonicities,, European Journal of Operational Research, 164 (2005), 115.  doi: 10.1016/j.ejor.2003.11.017.  Google Scholar

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D. H. Yuan, X. L. Liu and G. M. Lai, Note on generalized invex functions,, Optimization Letters, 7 (2013), 617.  doi: 10.1007/s11590-012-0446-z.  Google Scholar

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C. Zălinescu, A Critical View on Invexity,, Journal of Optimization Theory and Applications, (): 10957.  doi: DOI 10.1007/s10957-013-0506-2.  Google Scholar

show all references

References:
[1]

S. R. Mohan and S. K. Neogy, On invex sets and preinvex functions,, Journal of Mathematical Analysis and Applications, 189 (1995), 901.  doi: 10.1006/jmaa.1995.1057.  Google Scholar

[2]

X. M. Yang, X. Q. Yang and K. L. Teo, Characterizations and applications of prequasi-invex functions,, Journal of Optimization Theory and Applications, 110 (2001), 645.  doi: 10.1023/A:1017544513305.  Google Scholar

[3]

X. M. Yang, X. Q. Yang and K. L. Teo, Generalized invexity and generalized invariant monotonicity,, Journal of Optimization Theory and Applications, 117 (2003), 607.  doi: 10.1023/A:1023953823177.  Google Scholar

[4]

X. M. Yang, X. Q. Yang and K. L. Teo, Criteria for generalized invex monotonicities,, European Journal of Operational Research, 164 (2005), 115.  doi: 10.1016/j.ejor.2003.11.017.  Google Scholar

[5]

D. H. Yuan, X. L. Liu and G. M. Lai, Note on generalized invex functions,, Optimization Letters, 7 (2013), 617.  doi: 10.1007/s11590-012-0446-z.  Google Scholar

[6]

C. Zălinescu, A Critical View on Invexity,, Journal of Optimization Theory and Applications, (): 10957.  doi: DOI 10.1007/s10957-013-0506-2.  Google Scholar

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