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

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

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

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

Received April 2013 Revised August 2013 Published October 2013

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

References:

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References:

[1]	T. Antczak, (p,r)-invex sets and functions,, J. Math. Anal. Appl., 263 (2001), 355. doi: 10.1006/jmaa.2001.7574. Google Scholar
[2]	M. Avriel, r-convex functions,, Math. Programming, 2 (1972), 309. Google Scholar
[3]	A. Ben-Israel and B. Mond, What is invexity? , J. Aust. Math. Soc. Ser. B., 28 (1986), 1. doi: 10.1017/S0334270000005142. Google Scholar
[4]	X. Chen, Some properties of semi-E-convex functions,, J. Math. Anal. Appl., 275 (2002), 251. doi: 10.1016/S0022-247X(02)00325-6. Google Scholar
[5]	C. Fulga and V. Preda, Nonlinear programming with E-preinvex and local E-preinvex functions,, European J.Oper.Res., 192 (2009), 737. doi: 10.1016/j.ejor.2007.11.056. Google Scholar
[6]	M. A. Hanson, On sufficiency of the Kuhn-Tucker conditions,, J. Math. Anal. Appl., 80 (1981), 545. doi: 10.1016/0022-247X(81)90123-2. Google Scholar
[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. Google Scholar
[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. Google Scholar
[9]	S. R. Mohan and S. K. Neogy, On invex sets and preinvex functions,, J. Math. Anal. Appl., 189 (1995), 901. doi: 10.1006/jmaa.1995.1057. Google Scholar
[10]	R. Pini, Invexity and generalized convexity,, Optimization, 22 (1999), 513. doi: 10.1080/02331939108843693. Google Scholar
[11]	T. Weir and B. Mond, Preinvex functions in multiple objective optimization,, J. Math. Anal. Appl., 136 (1988), 29. doi: 10.1016/0022-247X(88)90113-8. Google Scholar
[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. doi: 10.1023/A:1017544513305. Google Scholar
[13]	E. A. Youness, E-convex sets, E-convex functions and E-convex programming,, J. Optim. Theory Appl., 102 (1999), 439. doi: 10.1023/A:1021792726715. Google Scholar
[14]	Y. Zhao and J. Y. Huang, Semi-strictly F-G generalized convex functions,, Journal of Chongqing Normal University(Natural Science), 28 (2011), 7. Google Scholar
[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. Google Scholar

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