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Generalized variational inequalities for maximal monotone operators

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Abstract

In this paper, we present some new results on the existence of solutions of generalized variational inequalities for set-valued mappings in reflexive Banach spaces with Fréchet differentiable norms. Moreover, the structure of the solution sets is investigated. The result obtained in this paper improves and extends the ones announced by Fang and Peterson [S. C. Fang and E. L. Peterson, Generalized Variational Inequalities, J. Optim. Theory Appl., 38 (1982), 363-383] and others.

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Acknowledgements

This work was supported by Vietnam National Foundation for Science and Technology Development (NAFOSTED) [Grant Number 101.02-2020.13], to which, the author would like to express many thanks.

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Authors and Affiliations

  1. Institute of Mathematics, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, Cau Giay, Hanoi, Vietnam

    Nguyen Quynh Nga

  2. Graduate University of Science and Technology, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, Cau Giay, Hanoi, Vietnam

    Nguyen Quynh Nga

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  1. Nguyen Quynh Nga
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Correspondence to Nguyen Quynh Nga.

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Communicated by G.D. Veerappa Gowda.

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Nga, N.Q. Generalized variational inequalities for maximal monotone operators. Indian J Pure Appl Math 52, 96–104 (2021). https://doi.org/10.1007/s13226-021-00118-4

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  • DOI: https://doi.org/10.1007/s13226-021-00118-4

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