American Institute of Mathematical Sciences

Advanced
2013, 3(4): 615-625. doi: 10.3934/naco.2013.3.615

Some properties of a class of $(F,E)$-$G$ generalized convex functions

Lijia Yan 1,

1. 

Department of Mathematics, Chongqing Normal University, Chongqing 400047, China

Received  April 2013 Revised  August 2013 Published  October 2013

In this paper, firstly, a new class of $(F,E)$-$G$ generalized convex functions, which is the generalization of $F$-$G$ generalized convex functions, is introduced. Secondly, some properties of $(F,E)$-$G$ generalized convex functions are obtained. Finally, some relations between $(F,E)$-$G$ generalized convex functions and other generalizations of convex functions are established.
Keywords: $F$-$G$ generalized convex functions, E)$ generalized convex set, $(F, E)$-$G$ quasiconvex functions., $F$ generalized convex set, $(F, E)$-$G$ generalized convex functions, $(F.
Mathematics Subject Classification: Primary: 90C26; Secondary: 90C3.
Citation: Lijia Yan. Some properties of a class of $(F,E)$-$G$ generalized convex functions. Numerical Algebra, Control and Optimization, 2013, 3 (4) : 615-625. doi: 10.3934/naco.2013.3.615
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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