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Some properties of a class of $(F,E)$-$G$ generalized convex functions
1. | Department of Mathematics, Chongqing Normal University, Chongqing 400047, China |
References:
[1] |
T. Antczak, (p,r)-invex sets and functions, J. Math. Anal. Appl., 263 (2001), 355-379.
doi: 10.1006/jmaa.2001.7574. |
[2] |
M. Avriel, r-convex functions, Math. Programming, 2 (1972), 309-323. |
[3] |
A. Ben-Israel and B. Mond, What is invexity? J. Aust. Math. Soc. Ser. B., 28 (1986), 1-9.
doi: 10.1017/S0334270000005142. |
[4] |
X. Chen, Some properties of semi-E-convex functions, J. Math. Anal. Appl., 275 (2002), 251-262.
doi: 10.1016/S0022-247X(02)00325-6. |
[5] |
C. Fulga and V. Preda, Nonlinear programming with E-preinvex and local E-preinvex functions, European J.Oper.Res., 192 (2009), 737-743.
doi: 10.1016/j.ejor.2007.11.056. |
[6] |
M. A. Hanson, On sufficiency of the Kuhn-Tucker conditions, J. Math. Anal. Appl., 80 (1981), 545-550.
doi: 10.1016/0022-247X(81)90123-2. |
[7] |
J. Y. Huang, Y. Zhao, D. Li and Y. J. Li, F-G generalized convex functions and semicontinuous functions, Journal of Hangzhou Normal University(Natural Science), 10 (2011), 223-247. |
[8] |
J. Y. Huang, Y. Zhao, and Y. N. Fang, The F-G generalized convex functions and F quasi convex functions, Journal of Chongqing Normal University(Natural Science), 28 (2011), 1-5. |
[9] |
S. R. Mohan and S. K. Neogy, On invex sets and preinvex functions, J. Math. Anal. Appl., 189 (1995), 901-908.
doi: 10.1006/jmaa.1995.1057. |
[10] |
R. Pini, Invexity and generalized convexity, Optimization, 22 (1999), 513-525.
doi: 10.1080/02331939108843693. |
[11] |
T. Weir and B. Mond, Preinvex functions in multiple objective optimization, J. Math. Anal. Appl., 136 (1988), 29-38.
doi: 10.1016/0022-247X(88)90113-8. |
[12] |
X. M. Yang, X. Q. Yang and K. L. Teo, Characterizations and applications of prequasi-invex functions, J. Optim. Theory Appl., 100 (2001), 645-668.
doi: 10.1023/A:1017544513305. |
[13] |
E. A. Youness, E-convex sets, E-convex functions and E-convex programming, J. Optim. Theory Appl., 102 (1999), 439-450.
doi: 10.1023/A:1021792726715. |
[14] |
Y. Zhao and J. Y. Huang, Semi-strictly F-G generalized convex functions, Journal of Chongqing Normal University(Natural Science), 28 (2011), 7-12. |
[15] |
Y. Zhao, J. Y. Huang and C. Y. Li, Strictly F-G generalized convex functions, Journal of Hangzhou Normal University(Natural Science), 10 (2011), 20-26. |
show all references
References:
[1] |
T. Antczak, (p,r)-invex sets and functions, J. Math. Anal. Appl., 263 (2001), 355-379.
doi: 10.1006/jmaa.2001.7574. |
[2] |
M. Avriel, r-convex functions, Math. Programming, 2 (1972), 309-323. |
[3] |
A. Ben-Israel and B. Mond, What is invexity? J. Aust. Math. Soc. Ser. B., 28 (1986), 1-9.
doi: 10.1017/S0334270000005142. |
[4] |
X. Chen, Some properties of semi-E-convex functions, J. Math. Anal. Appl., 275 (2002), 251-262.
doi: 10.1016/S0022-247X(02)00325-6. |
[5] |
C. Fulga and V. Preda, Nonlinear programming with E-preinvex and local E-preinvex functions, European J.Oper.Res., 192 (2009), 737-743.
doi: 10.1016/j.ejor.2007.11.056. |
[6] |
M. A. Hanson, On sufficiency of the Kuhn-Tucker conditions, J. Math. Anal. Appl., 80 (1981), 545-550.
doi: 10.1016/0022-247X(81)90123-2. |
[7] |
J. Y. Huang, Y. Zhao, D. Li and Y. J. Li, F-G generalized convex functions and semicontinuous functions, Journal of Hangzhou Normal University(Natural Science), 10 (2011), 223-247. |
[8] |
J. Y. Huang, Y. Zhao, and Y. N. Fang, The F-G generalized convex functions and F quasi convex functions, Journal of Chongqing Normal University(Natural Science), 28 (2011), 1-5. |
[9] |
S. R. Mohan and S. K. Neogy, On invex sets and preinvex functions, J. Math. Anal. Appl., 189 (1995), 901-908.
doi: 10.1006/jmaa.1995.1057. |
[10] |
R. Pini, Invexity and generalized convexity, Optimization, 22 (1999), 513-525.
doi: 10.1080/02331939108843693. |
[11] |
T. Weir and B. Mond, Preinvex functions in multiple objective optimization, J. Math. Anal. Appl., 136 (1988), 29-38.
doi: 10.1016/0022-247X(88)90113-8. |
[12] |
X. M. Yang, X. Q. Yang and K. L. Teo, Characterizations and applications of prequasi-invex functions, J. Optim. Theory Appl., 100 (2001), 645-668.
doi: 10.1023/A:1017544513305. |
[13] |
E. A. Youness, E-convex sets, E-convex functions and E-convex programming, J. Optim. Theory Appl., 102 (1999), 439-450.
doi: 10.1023/A:1021792726715. |
[14] |
Y. Zhao and J. Y. Huang, Semi-strictly F-G generalized convex functions, Journal of Chongqing Normal University(Natural Science), 28 (2011), 7-12. |
[15] |
Y. Zhao, J. Y. Huang and C. Y. Li, Strictly F-G generalized convex functions, Journal of Hangzhou Normal University(Natural Science), 10 (2011), 20-26. |
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