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 & 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.  Google Scholar

[2]

M. Avriel, r-convex functions, Math. Programming, 2 (1972), 309-323.  Google Scholar

[3]

A. Ben-Israel and B. Mond, What is invexity? J. Aust. Math. Soc. Ser. B., 28 (1986), 1-9. doi: 10.1017/S0334270000005142.  Google Scholar

[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.  Google Scholar

[5]

C. Fulga and V. Preda, Nonlinear programming with E-preinvex and local E-preinvex functions, European J.Oper.Res., 192 (2009), 737-743. 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), 545-550. 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), 223-247. 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), 1-5. Google Scholar

[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.  Google Scholar

[10]

R. Pini, Invexity and generalized convexity, Optimization, 22 (1999), 513-525. doi: 10.1080/02331939108843693.  Google Scholar

[11]

T. Weir and B. Mond, Preinvex functions in multiple objective optimization, J. Math. Anal. Appl., 136 (1988), 29-38. 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), 645-668. 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), 439-450. 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), 7-12. 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), 20-26. Google Scholar

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.  Google Scholar

[2]

M. Avriel, r-convex functions, Math. Programming, 2 (1972), 309-323.  Google Scholar

[3]

A. Ben-Israel and B. Mond, What is invexity? J. Aust. Math. Soc. Ser. B., 28 (1986), 1-9. doi: 10.1017/S0334270000005142.  Google Scholar

[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.  Google Scholar

[5]

C. Fulga and V. Preda, Nonlinear programming with E-preinvex and local E-preinvex functions, European J.Oper.Res., 192 (2009), 737-743. 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), 545-550. 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), 223-247. 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), 1-5. Google Scholar

[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.  Google Scholar

[10]

R. Pini, Invexity and generalized convexity, Optimization, 22 (1999), 513-525. doi: 10.1080/02331939108843693.  Google Scholar

[11]

T. Weir and B. Mond, Preinvex functions in multiple objective optimization, J. Math. Anal. Appl., 136 (1988), 29-38. 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), 645-668. 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), 439-450. 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), 7-12. 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), 20-26. Google Scholar

[1]

Leandro M. Del Pezzo, Nicolás Frevenza, Julio D. Rossi. Convex and quasiconvex functions in metric graphs. Networks & Heterogeneous Media, 2021, 16 (4) : 591-607. doi: 10.3934/nhm.2021019
[2]

Seppo Granlund, Niko Marola. Phragmén--Lindelöf theorem for infinity harmonic functions. Communications on Pure & Applied Analysis, 2015, 14 (1) : 127-132. doi: 10.3934/cpaa.2015.14.127
[3]

Orit Lavi, Doron Ginsberg, Yoram Louzoun. Regulation of modular Cyclin and CDK feedback loops by an E2F transcription oscillator in the mammalian cell cycle. Mathematical Biosciences & Engineering, 2011, 8 (2) : 445-461. doi: 10.3934/mbe.2011.8.445
[4]

Xiuhong Chen, Zhihua Li. On optimality conditions and duality for non-differentiable interval-valued programming problems with the generalized (F, ρ)-convexity. Journal of Industrial & Management Optimization, 2018, 14 (3) : 895-912. doi: 10.3934/jimo.2017081
[5]

Nguyen Thi Bach Kim, Nguyen Canh Nam, Le Quang Thuy. An outcome space algorithm for minimizing the product of two convex functions over a convex set. Journal of Industrial & Management Optimization, 2013, 9 (1) : 243-253. doi: 10.3934/jimo.2013.9.243
[6]

Byung-Soo Lee. A convergence theorem of common fixed points of a countably infinite family of asymptotically quasi-$f_i$-expansive mappings in convex metric spaces. Numerical Algebra, Control & Optimization, 2013, 3 (3) : 557-565. doi: 10.3934/naco.2013.3.557
[7]

Anulekha Dhara, Aparna Mehra. Conjugate duality for generalized convex optimization problems. Journal of Industrial & Management Optimization, 2007, 3 (3) : 415-427. doi: 10.3934/jimo.2007.3.415
[8]

David Keyes. $\mathbb F_p$-codes, theta functions and the Hamming weight MacWilliams identity. Advances in Mathematics of Communications, 2012, 6 (4) : 401-418. doi: 10.3934/amc.2012.6.401
[9]

Małgorzata Wyrwas, Dorota Mozyrska, Ewa Girejko. Subdifferentials of convex functions on time scales. Discrete & Continuous Dynamical Systems, 2011, 29 (2) : 671-691. doi: 10.3934/dcds.2011.29.671
[10]

Gregorio Díaz, Jesús Ildefonso Díaz. On the free boundary associated with the stationary Monge--Ampère operator on the set of non strictly convex functions. Discrete & Continuous Dynamical Systems, 2015, 35 (4) : 1447-1468. doi: 10.3934/dcds.2015.35.1447
[11]

Chao Deng, Xiaohua Yao. Well-posedness and ill-posedness for the 3D generalized Navier-Stokes equations in $\dot{F}^{-\alpha,r}_{\frac{3}{\alpha-1}}$. Discrete & Continuous Dynamical Systems, 2014, 34 (2) : 437-459. doi: 10.3934/dcds.2014.34.437
[12]

Dimitra Antonopoulou, Georgia Karali. Existence of solution for a generalized stochastic Cahn-Hilliard equation on convex domains. Discrete & Continuous Dynamical Systems - B, 2011, 16 (1) : 31-55. doi: 10.3934/dcdsb.2011.16.31
[13]

Fan Jiang, Zhongming Wu, Xingju Cai. Generalized ADMM with optimal indefinite proximal term for linearly constrained convex optimization. Journal of Industrial & Management Optimization, 2020, 16 (2) : 835-856. doi: 10.3934/jimo.2018181
[14]

Gang Li, Lipu Zhang, Zhe Liu. The stable duality of DC programs for composite convex functions. Journal of Industrial & Management Optimization, 2017, 13 (1) : 63-79. doi: 10.3934/jimo.2016004
[15]

Zhongliang Deng, Enwen Hu. Error minimization with global optimization for difference of convex functions. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 1027-1033. doi: 10.3934/dcdss.2019070
[16]

Khalida Inayat Noor, Muhammad Aslam Noor. Higher order uniformly close-to-convex functions. Discrete & Continuous Dynamical Systems - S, 2015, 8 (6) : 1277-1290. doi: 10.3934/dcdss.2015.8.1277
[17]

W. Cary Huffman. On the theory of $\mathbb{F}_q$-linear $\mathbb{F}_{q^t}$-codes. Advances in Mathematics of Communications, 2013, 7 (3) : 349-378. doi: 10.3934/amc.2013.7.349
[18]

Fernando Alcalde Cuesta, Ana Rechtman. Minimal Følner foliations are amenable. Discrete & Continuous Dynamical Systems, 2011, 31 (3) : 685-707. doi: 10.3934/dcds.2011.31.685
[19]

William E. Fitzgibbon. The work of Glenn F. Webb. Mathematical Biosciences & Engineering, 2015, 12 (4) : v-xvi. doi: 10.3934/mbe.2015.12.4v
[20]

Jiao Du, Longjiang Qu, Chao Li, Xin Liao. Constructing 1-resilient rotation symmetric functions over $ {\mathbb F}_{p} $ with $ {q} $ variables through special orthogonal arrays. Advances in Mathematics of Communications, 2020, 14 (2) : 247-263. doi: 10.3934/amc.2020018

 Impact Factor: 

Tools

Metrics

  • PDF downloads (68)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences | Privacy Policy