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Remark on cone semistrictly preinvex functions

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Abstract

In this paper, we consider the cone semistrictly preinvex function introduced by Peng and Zhu (J Inequal Appl 93532:1–14, 2006). The relationship between cone semistrictly preinvex functions and cone preinvex functions is investigated. A property of the cone semistrictly preinvex function is obtained.

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References

  1. Craven B.D.: Invex functions and constrained local minima. Bull. Aust. Math. Soc. 24, 357–366 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  2. Hanson M.A.: On sufficiency of the Kuhn–Tucker conditions. J. Math. Anal. Appl. 80, 545–550 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  3. Kazmi K.R.: Some remarks on vector optimization problems. J. Optim. Theory Appl. 96, 133–138 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  4. Long X.J., Peng J.W.: Semi-B-preinvex functions. J. Optim. Theory Appl. 131, 301–305 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  5. Mishra S.K., Giorgi G.: Invexity and Optimization, Nonconvex Optimization and Its Applications, vol. 88. Springer, Berlin (2008)

    Google Scholar 

  6. Mohan S.R., Neogy S.K.: On invex sets and preinvex functions. J. Math. Anal. Appl. 189, 901–908 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  7. Peng, J.W., Zhu, D.L.: On D-preinvex-type functions. J. Inequal. Appl. 93532, 1–14 (2006)

    Google Scholar 

  8. Weir T., Jeyakumar V.: A class of nonconvex functions and mathematical programming. Bull. Aust. Math. Soc. 38, 177–189 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  9. Weir T., Mond B.: Preinvex functions in multiple-objective optimization. J. Math. Anal. Appl. 136, 29–38 (1988)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  11. Yang X.M., Yang X.Q., Teo K.L.: Explicitly B-preinvex functions. J. Comput. Appl. Math. 146, 25–36 (2002)

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. College of Mathematics and Statistics, Chongqing Technology and Business University, 400067, Chongqing, People’s Republic of China

    X. J. Long

  2. College of Science, Chongqing JiaoTong University, 400067, Chongqing, People’s Republic of China

    Z. Y. Peng

  3. Commercial Planning College, Chongqing Technology and Business University, 400067, Chongqing, People’s Republic of China

    B. Zeng

Authors
  1. X. J. Long
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  2. Z. Y. Peng
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  3. B. Zeng
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Correspondence to X. J. Long.

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Long, X.J., Peng, Z.Y. & Zeng, B. Remark on cone semistrictly preinvex functions. Optim Lett 3, 337–345 (2009). https://doi.org/10.1007/s11590-008-0113-6

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  • DOI: https://doi.org/10.1007/s11590-008-0113-6

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