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Generalized Invexity and Generalized Invariant Monotonicity

Author

Listed:
  • X.M. Yang

    (Chongqing Normal University)

  • X.Q. Yang

    (Hong Kong Polytechnic University)

  • K.L. Teo

    (Hong Kong Polytechnic University)

Abstract

In this paper, several kinds of invariant monotone maps and generalized invariant monotone maps are introduced. Some examples are given which show that invariant monotonicity and generalized invariant monotonicity are proper generalizations of monotonicity and generalized monotonicity. Relationships between generalized invariant monotonicity and generalized invexity are established. Our results are generalizations of those presented by Karamardian and Schaible.

Suggested Citation

  • X.M. Yang & X.Q. Yang & K.L. Teo, 2003. "Generalized Invexity and Generalized Invariant Monotonicity," Journal of Optimization Theory and Applications, Springer, vol. 117(3), pages 607-625, June.
    • Handle: RePEc:spr:joptap:v:117:y:2003:i:3:d:10.1023_a:1023953823177
    DOI: 10.1023/A:1023953823177
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    References listed on IDEAS

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    1. Ruiz-Garzon, G. & Osuna-Gomez, R. & Rufian-Lizana, A., 2003. "Generalized invex monotonicity," European Journal of Operational Research, Elsevier, vol. 144(3), pages 501-512, February.
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    Cited by:

    1. X. M. Yang, 2009. "On Characterizing the Solution Sets of Pseudoinvex Extremum Problems," Journal of Optimization Theory and Applications, Springer, vol. 140(3), pages 537-542, March.
    2. M. Soleimani-damaneh, 2012. "Characterizations and applications of generalized invexity and monotonicity in Asplund spaces," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(3), pages 592-613, October.
    3. Constantin Zălinescu, 2014. "A Critical View on Invexity," Journal of Optimization Theory and Applications, Springer, vol. 162(3), pages 695-704, September.
    4. Peng, Jian-Wen, 2006. "Criteria for generalized invex monotonicities without Condition C," European Journal of Operational Research, Elsevier, vol. 170(2), pages 667-671, April.
    5. D. L. Zhu & L. L. Zhu & Q. Xu, 2008. "Generalized Invex Monotonicity and Its Role in Solving Variational-Like Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 137(2), pages 453-464, May.
    6. Qamrul Ansari & Mahboubeh Rezaie & Jafar Zafarani, 2012. "Generalized vector variational-like inequalities and vector optimization," Journal of Global Optimization, Springer, vol. 53(2), pages 271-284, June.
    7. Noor, Muhammad Aslam & Noor, Khalida Inayat & Awan, Muhammad Uzair, 2015. "Some quantum integral inequalities via preinvex functions," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 242-251.
    8. Zaiyun Peng & Yawei Liu & X. J. Long, 2009. "Remarks on New Properties of Preinvex Functions," Modern Applied Science, Canadian Center of Science and Education, vol. 3(11), pages 1-11, November.
    9. Akhlad Iqbal & Shahid Ali & I. Ahmad, 2012. "On Geodesic E-Convex Sets, Geodesic E-Convex Functions and E-Epigraphs," Journal of Optimization Theory and Applications, Springer, vol. 155(1), pages 239-251, October.
    10. Yang, X. M. & Yang, X. Q. & Teo, K. L., 2005. "Criteria for generalized invex monotonicities," European Journal of Operational Research, Elsevier, vol. 164(1), pages 115-119, July.
    11. S. Al-Homidan & Q. H. Ansari, 2010. "Generalized Minty Vector Variational-Like Inequalities and Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 144(1), pages 1-11, January.
    12. Muhammad Bilal Khan & Gustavo Santos-García & Muhammad Aslam Noor & Mohamed S. Soliman, 2022. "New Class of Preinvex Fuzzy Mappings and Related Inequalities," Mathematics, MDPI, vol. 10(20), pages 1-20, October.

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