Skip to main content
Log in

D-B-Preinvex Type Mappings

  • Published:
Journal of Systems Science and Complexity Aims and scope Submit manuscript

Abstract

In this paper, such new definitions as D-B-preinvexity, strictly D-B-preinvexity and explicitly D-B-preinvexity for vector-valued mappings are firstly introduced. Then, a sufficient condition of D-B-preinvex mappings is shown. And then the relationship between the explicitly D-B-preinvexity and the strictly D-B-preinvexity is discussed. Finally, some properties of D-B-preinvex type mappings are given.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. T. Weir and B. Mond, Pre-invex functions in multiple objective optimization, J. Math. Anal. Appl., 1988, 136: 29–38.

    Article  Google Scholar 

  2. T. Weir and V. Jeyakumar, A class of nonconvex functions and mathematical programming, Bulletin of the Australian Mathematical Society, 1988, 38: 177–189.

    Google Scholar 

  3. X. M. Yang and D. Li, On properties of preinvex functions, J. Math. Anal. Appl., 2001, 256: 229–241.

    Article  Google Scholar 

  4. X. M. Yang and D. Li, Semistrictly preinvex functions, J. Math. Anal. Appl., 2001, 258: 287–308.

    Article  Google Scholar 

  5. C. R. Bector, S. K. Suneja and C. S. Lalitha, Generalized B-vex functions and generalized B-vex programming, J. Optim. Theory Appl., 1993, 76: 561–576.

    Article  Google Scholar 

  6. S. K. Suneja, C. Singh and C. R. Bector, Generalization of preinvex and B-vex functions, J. Optim. Theory Appl., 1993, 76: 577–587.

    Article  Google Scholar 

  7. C. R. Bector and C. Singh, B-vex functions, J. Optim. Theory Appl., 1991, 71: 237–253.

    Article  Google Scholar 

  8. X. M. Yang, X. Q. Yang and K. L. Teo, Explicitly B-preinvex functions, J. Comp. Appl. Math., 2002, 146: 25–36.

    Article  Google Scholar 

  9. S. R. Mohan and S. K. Neogy, On invex set and preinvex functions, J. Math. Anal. Appl., 1995, 189: 901–908.

    Article  Google Scholar 

  10. V. Jeyakumar, W. Oettli and M. Natividad, A solvability theorem for a class of quasiconvex mappings with applications to optimization, J. Math. Anal. Appl., 1993, 179: 537–546.

    Article  Google Scholar 

  11. T. Tanaka, Generalized semicontinuity and existence theorems for cone saddle points, Appl. Math. Optim., 1997, 36: 313–322.

    Article  Google Scholar 

  12. D. T. Luc, Theory of Vector Optimization, Springer-Verlag, Berlin, 1989.

    Google Scholar 

  13. X. M. Yang, Semistrictly convex function, Opsearch, 1994, 31: 15–27.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jianwen Peng.

Additional information

This research was supported by the National Natural Science Foundation of China (Grant No. 10171118), the Education Committee Project Research Foundation of Chongqing (Grant No. 030801), the Natural Science Foundation of Chongqing (No. 8409) and the Inland Education Foundation of Chongqing.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Peng, J., Yang, X. & Rong, W. D-B-Preinvex Type Mappings. Jrl Syst Sci & Complex 19, 93–100 (2006). https://doi.org/10.1007/s11424-006-0093-5

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11424-006-0093-5

Key Words

Navigation