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Generalized Nonsmooth Exponential-Type Vector Variational-Like Inequalities and Nonsmooth Vector Optimization Problems in Asplund Spaces

Author

Listed:
  • Syed Shakaib Irfan

    (College of Engineering, Qassim University, Buraidah 51452, Al-Qassim, Saudi Arabia
    These authors contributed equally to this work.)

  • Mijanur Rahaman

    (Department of Mathematics, Aligarh Muslim University, Aligarh-202002, India
    These authors contributed equally to this work.)

  • Iqbal Ahmad

    (College of Engineering, Qassim University, Buraidah 51452, Al-Qassim, Saudi Arabia)

  • Rais Ahmad

    (Department of Mathematics, Aligarh Muslim University, Aligarh-202002, India
    These authors contributed equally to this work.)

  • Saddam Husain

    (Department of Mathematics, Aligarh Muslim University, Aligarh-202002, India
    These authors contributed equally to this work.)

Abstract

The aim of this article is to study new types of generalized nonsmooth exponential type vector variational-like inequality problems involving Mordukhovich limiting subdifferential operator. We establish some relationships between generalized nonsmooth exponential type vector variational-like inequality problems and vector optimization problems under some invexity assumptions. The celebrated Fan-KKM theorem is used to obtain the existence of solution of generalized nonsmooth exponential-type vector variational like inequality problems. In support of our main result, some examples are given. Our results presented in this article improve, extend, and generalize some known results offer in the literature.

Suggested Citation

  • Syed Shakaib Irfan & Mijanur Rahaman & Iqbal Ahmad & Rais Ahmad & Saddam Husain, 2019. "Generalized Nonsmooth Exponential-Type Vector Variational-Like Inequalities and Nonsmooth Vector Optimization Problems in Asplund Spaces," Mathematics, MDPI, vol. 7(4), pages 1-11, April.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:4:p:345-:d:221706
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    References listed on IDEAS

    as
    1. X. M. Yang & X. Q. Yang & K. L. Teo, 2004. "Some Remarks on the Minty Vector Variational Inequality," Journal of Optimization Theory and Applications, Springer, vol. 121(1), pages 193-201, April.
    2. Antczak, Tadeusz, 2004. "(p,r)-Invexity in multiobjective programming," European Journal of Operational Research, Elsevier, vol. 152(1), pages 72-87, January.
    3. Q. H. Ansari & G. M. Lee, 2010. "Nonsmooth Vector Optimization Problems and Minty Vector Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 145(1), pages 1-16, April.
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