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A remark on preinvex functions

Published online by Cambridge University Press:  17 April 2009

Jianwen Peng  and
Xianjun Long
Jianwen Peng
Affiliation:
College of Mathematics and Computer Science, Chongqing Normal University, Chongqing 400047, Peoples Republic of China, e-mail: [email protected] of Mathematics, Inner Mongolia University, Hohhot 010021, Inner Mongolia, Peoples Republic of China
Xianjun Long
Affiliation:
College of Mathematics and Compute Science, Chongqing Normal University, Chongqing 400047, Peoples Republic of China
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In this paper, we show that the ratio of preinvex functions is invex. Hence, we give a positive answer to the open question which was proposed in a paper of Yang, Yang and Teo in (2003).

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 70 , Issue 3 , December 2004 , pp. 397 - 400
Copyright
Copyright © Australian Mathematical Society 2004

References

[1]Yang, X.M., Yang, X.Q. and Teo, K.L., ‘On properties of semipreinvex function’, Bull. Austral. Math. Soc. 68 (2003), 449–459.CrossRefGoogle Scholar
[2]Hanson, M.A., ‘On sufficiency of the Kuhn-Tuker conditions’, Math. Anal. Appl. 80 (1981), 544–550.CrossRefGoogle Scholar
[3]Craven, B.D., ‘Invex functions and constrained local minima’, Bull. Austral. Math. Soc. 24 (1981), 357–366.CrossRefGoogle Scholar
[4]Weir, T. and Mond, B., ‘Pre-invex functions in multiple objective optimizaton’, J. Math. Anal. Appl. 136 (1988), 29–38.CrossRefGoogle Scholar
[5]Weir, T. and Jeyakumar, V., ‘A class of nonconvex functions and mathematical programming’, Bull. Austral. Math. Soc. 38 (1988), 177–189.CrossRefGoogle Scholar
[6]Yang, X.Q. and Chen, G.Y., ‘A class of nonconvex functions and pre-variational inequalities’, J. Math. Anal. Appl. 169 (1992), 359–373.Google Scholar
[7]Khan, Z.A. and Hanson, M.A., ‘On retio of invexity in mathematical programming’, J. Math. Anal. Appl. 205 (1997), 330–336.CrossRefGoogle Scholar
[8]Craven, B.D. and Mond, B., ‘Fractional programming with invexity’, in Progress in optimization, Appl. Optim. 30 (Kluwer Acad. Publ., Dordrecht, 1999), pp. 79–89.CrossRefGoogle Scholar